Lecture 15 Symmetric matrices, quadratic forms, matrix

目录方程组的几何解释 (2)矩阵消元 (3)乘法和逆矩阵 (4)A的LU分解 (6)转置-置换-向量空间R (8)求解AX=0：主变量，特解 (9)求解AX=b：可解性和解的解构 (10)线性相关性、基、维数 (11)四个基本子空间 (12)矩阵空间、秩1矩阵和小世界图 (13)图和网络 (14)正交向量与子空间 (15)子空间投影 (18)投影矩阵与最小二乘 (20)正交矩阵和Gram-Schmidt正交化 (21)特征值与特征向量 (27)对角化和A的幂 (28)微分方程和exp(At)（待处理） (29)对称矩阵与正定性 (29)正定矩阵与最小值 (31)相似矩阵和若尔当型（未完成） (32)奇异值分解(SVD) (33)线性变换及对应矩阵 (34)基变换和图像压缩 (36)NOTATIONp：projection vectorP：projection matrixe：error vectorP：permutation matrixT：transport signC(A)：column spaceN(A)：null spaceU：upper triangularL：lower triangularE：elimination matrixQ：orthogonal matrix, which means the column vectors are orthogonalE：elementary/elimination matrix, which always appears in the elimination of matrix N：null space matrix, the “solution matrix” of AX=0R：reduced matrix, which always appears in the triangular matrix, “IF00”I：identity matrixS：eigenvector matrixΛ：eigenvalue matrixC：cofactor matrix关于LINER ALGEBA名垂青史的分析方法：由具象到抽象，由二维到高维。

数学英语词汇adjont(adjugate) of matrix A（A的伴随矩阵）augmented matrix A（A的增广矩阵）block diagonal matrix（块对角矩阵）block matrix（块矩阵）basic solution set（基础解系）Cauchy-Schwarz inequality（柯西-许瓦兹不等式）characteristic equation（特征方程）characteristic polynomial（特征多项式）coffcient matrix（系数矩阵）cofactor（代数余子式）cofactor expansion（代数余子式展开）column vector（列向量）commuting matrices（交换矩阵）consistent linear system（相容线性方程组）Cramer’s rule（克莱姆法则）Cross-product term（交叉项）Determinant（行列式）Diagonal entries（对角元素）Diagonal matrix（对角矩阵）Dimension of a vector space V（向量空间V的维数）echelon matrix（梯形矩阵）eigenspace（特征空间）eigenvalue（特征值）eigenvector（特征向量）eigenvector basis（特征向量的基）elementary matrix（初等矩阵）elementary row operations（行初等变换）full rank（满秩）fundermental set of solution（基础解系）grneral solution（通解）Gram-Schmidt process（施密特正交化过程）homogeneous linear equations（齐次线性方程组）identity matrix（单位矩阵）inconsistent linear system（不相容线性方程组）indefinite matrix（不定矩阵）indefinit quatratic form（不定二次型）infinite-dimensional space（无限维空间）inner product（内积）linear combination（线性组合）linearly dependent（线性相关）linearly independent（线性无关）linear transformation（线性变换）lower triangular matrix（下三角形矩阵）matrix（矩阵）negative definite quaratic form（负定二次型）negative semidefinite quadratic form（半负定二次型）nonhomogeneous equations（非齐次线性方程组）nonsigular matrix（非奇异矩阵）nontrivial solution（非平凡解）norm of vector V（向量V的范数）orthogonal basis（正交基）orthogonal complement（正交补）orthogonal decomposition（正交分解）orthogonally diagonalizable matrix（矩阵的正交对角化）orthogonal matrix（正交矩阵）orthogonal set（正交向量组）orthonormal basis（规范正交基）orthonomal set（规范正交向量组）partitioned matrix（分块矩阵）positive definite matrix（正定矩阵）positive definite quatratic form（正定二次型）positive semidefinite matrix（半正定矩阵）positive semidefinite quadratic form（半正定二次型）quatratic form（二次型）rank of matrix A（矩阵A的秩）reduced echelon matrix（最简梯形阵）row vector（行向量）similar matrices（相似矩阵）similarity transformation（相似变换）singular matrix（奇异矩阵）solution set（解集合）standard basis（标准基）standard matrix（标准矩阵）submatrix（子矩阵）subspace（子空间）symmetric matrix（对称矩阵）trace of matrix A（矩阵A的迹）transpose of A（矩阵A的转秩）triangle inequlity（三角不等式）trivial solution（平凡解）unit vector（单位向量）upper triangular matrix（上三角形矩阵）vandermonde matrix（范得蒙矩阵）vector（向量）vector space（向量空间）zero subspace（零子空间）zero vector（零空间）absolute value（绝对值）accept（接受）acceptable region（接受域）additivity（可加性）adjusted（调整的）alternative hypothesis（对立假设）analysis（分析）analysis of covariance（协方差分析）analysis of variance（方差分析）arithmetic mean（算术平均值）association（相关性）assumption（假设）assumption checking（假设检验）availability（有效度）average（均值）balanced（平衡的）band（带宽）bar chart（条形图）beta-distribution（贝塔分布）between groups（组间的）bias（偏倚）binomial distribution（二项分布）binomial test（二项检验）calculate（计算）case（个案）category（类别）center of gravity（重心）central tendency（中心趋势）chi-square distribution（卡方分布）chi-square test（卡方检验）classify（分类）cluster analysis（聚类分析）coefficient（系数）coefficient of correlation（相关系数）collinearity（共线性）column（列）compare（比较）comparison（对照）components（构成，分量）compound（复合的）confidence interval（置信区间）consistency（一致性）constant（常数）continuous variable（连续变量）control charts（控制图）correlation（相关）covariance（协方差）covariance matrix（协方差矩阵）critical point（临界点）critical value（临界值）crosstab（列联表）cubic（三次的，立方的）cubic term（三次项）cumulative distribution function（累加分布函数）curve estimation（曲线估计）data（数据）default（默认的）definition（定义）deleted residual（剔除残差）density function（密度函数）dependent variable（因变量）description（描述）design of experiment（试验设计）deviations（差异）df. (degree of freedom)（自由度）diagnostic（诊断）dimension（维）discrete variable（离散变量）discriminant function（判别函数）discriminatory analysis（判别分析）distance（距离）distribution（分布）D-optimal design（D-优化设计）eaqual（相等）effects of interaction（交互效应）efficiency（有效性）eigenvalue（特征值）equal size（等含量）equation（方程）error（误差）estimate（估计）estimation of parameters（参数估计）estimations（估计量）evaluate（衡量）exact value（精确值）expectation（期望）expected value（期望值）exponential（指数的）exponential distributon（指数分布）extreme value（极值）factor（因素，因子）factor analysis（因子分析）factor score（因子得分）factorial designs（析因设计）factorial experiment（析因试验）fitted line（拟合线）fitted value（拟合值）fixed model（固定模型）fixed variable（固定变量）fractional factorial design（部分析因设计）frequency（频数）F-test（F检验）full factorial design（完全析因设计）function（函数）gamma distribution（伽玛分布）geometric mean（几何均值）group（组）harmomic mean（调和均值）heterogeneity（不齐性）histogram（直方图）homogeneity（齐性）homogeneity of variance（方差齐性）hypothesis（假设）hypothesis test（假设检验）independence（独立）independent variable（自变量）independent-samples（独立样本）index of correlation（相关指数）interaction（交互作用）interclass correlation（组内相关）interval estimate（区间估计）intraclass correlation（组间相关）inverse（倒数的）iterate（迭代）kernal（核）Kolmogorov-Smirnov test（柯尔莫哥洛夫-斯米诺夫检验）Kurtosis（峰度large sample problem（大样本问题）layer（层）least-significant difference（最小显著差数）least-square estimation（最小二乘估计）least-square method（最小二乘法）level（水平）level of significance（显著性水平）leverage value（中心化杠杆值）life（寿命）life test（寿命试验）likelihood function（似然函数）likelihood ratio test（似然比检验）linear（线性的）linear estimator（线性估计）linear model（线性模型）linear regression（线性回归）linear relation（线性关系）linear term（线性项）logarithmic（对数的）logarithms（对数）logistic（逻辑的）lost function（损失函数）main effect（主效应）matrix（矩阵）maximum（最大值）maximum likelihood estimation（极大似然估计）mean squared deviation(MSD)（均方差）mean sum of square（均方和）measure（衡量）media（中位数）M-estimator（M估计）minimum（最小值）missing values（缺失值）mixed model（混合模型）mode（众数）model（模型）Monte Carle method（蒙特卡罗法）moving average（移动平均值）multicollinearity（多元共线性）multiple comparison（多重比较）multiple correlation（多重相关）multiple correlation coefficient（复相关系数）multiple correlation coefficient（多元相关系数）multiple regression analysis（多元回归分析）multiple regression equation（多元回归方程）multiple response（多响应）multivariate analysis（多元分析）negative relationship（负相关）nonadditively（不可加性）nonlinear（非线性）nonlinear regression（非线性回归）noparametric tests（非参数检验）normal distribution（正态分布）null hypothesis（零假设）number of cases（个案数）one-sample（单样本）one-tailed test（单侧检验）one-way ANOVA（单向方差分析）one-way classification（单向分类）optimal（优化的）optimum allocation（最优配制）order（排序）order statistics（次序统计量）origin（原点）orthogonal（正交的）outliers（异常值）paired observations（成对观测数据）paired-sample（成对样本）parameter（参数）parameter estimation（参数估计）partial correlation（偏相关）partial correlation coefficient（偏相关系数）partial regression coefficient（偏回归系数）percent（百分数）percentiles（百分位数）pie chart（饼图）point estimate（点估计）poisson distribution（泊松分布）polynomial curve（多项式曲线）polynomial regression（多项式回归）polynomials（多项式）positive relationship（正相关）power（幂）P-P plot（P-P概率图）predict（预测）predicted value（预测值）prediction intervals（预测区间）principal component analysis（主成分分析）proability（概率）probability density function（概率密度函数）probit analysis（概率分析）proportion（比例）qadratic（二次的）Q-Q plot（Q-Q概率图）quadratic term（二次项）quality control（质量控制）quantitative（数量的，度量的）quartiles（四分位数）random（随机的）random number（随机数）random sampling（随机取样）random seed（随机数种子）random variable（随机变量）randomization（随机化）range（极差）rank（秩）rank correlation（秩相关）rank statistic（秩统计量）regression analysis（回归分析）regression coefficient（回归系数）regression line（回归线）reject（拒绝）rejection region（拒绝域）relationship（关系）reliability（可靠性）repeated（重复的）report（报告，报表）residual（残差）residual sum of squares（剩余平方和）response（响应）risk function（风险函数）robustness（稳健性）root mean square（标准差）row（行）run（游程）run test（游程检验）sample（样本）sample size（样本容量）sample space（样本空间）sampling（取样）sampling inspection（抽样检验）scatter chart（散点图）S-curve（S形曲线）separately（单独地）sets（集合）sign test（符号检验）significance（显著性）significance level（显著性水平）significance testing（显著性检验）significant（显著的，有效的）significant digits（有效数字）skewed distribution（偏态分布）skewness（偏度）small sample problem（小样本问题）smooth（平滑）sort（排序）soruces of variation（方差来源）space（空间）spread（扩展）square（平方）standard deviation（标准离差）standard error of mean（均值的标准误差）standardization（标准化）standardize（标准化）statistic（统计量）statistical quality control（统计质量控制）stepwise regression analysis（逐步回归）stimulus（刺激）strong assumption（强假设）stud. deleted residual（学生化剔除残差）stud. residual（学生化残差）subsamples（次级样本）sufficient statistic（充分统计量）sum（和）sum of squares（平方和）summary（概括，综述）table（表）t-distribution（t分布）test（检验）test criterion（检验判据）test for linearity（线性检验）test of goodness of fit（拟合优度检验）test of homogeneity（齐性检验）test of independence（独立性检验）test rules（检验法则）test statistics（检验统计量）testing function（检验函数）time series（时间序列）tolerance limits（容许限）total（总共，和）transformation（转换）treatment（处理）trimmed mean（截尾均值）true value（真值）t-test（t检验）two-tailed test（双侧检验）unbalanced（不平衡的）unbiased estimation（无偏估计）unbiasedness（无偏性）uniform distribution（均匀分布）value of estimator（估计值）variable（变量）variance（方差）variance components（方差分量）variance ratio（方差比）various（不同的）vector（向量）weight（加权，权重）weighted average（加权平均值）within groups（组内的）Z score （Z分数）。

英语词汇-数学词汇abbreviation 简写符号；简写 abscissa 横坐标absolute complement 绝对补集 absolute error 绝对误差absolute inequality 绝不等式 absolute maximum 绝对极大值absolute minimum 绝对极小值 absolute monotonic 绝对单调absolute value 绝对值 accelerate 加速acceleration 加速度acceleration due to gravity 重力加速度; 地心加速度accumulation 累积 accumulative 累积的accuracy 准确度 act on 施于action 作用; 作用力 acute angle 锐角acute-angled triangle 锐角三角形 add 加addition 加法 addition formula 加法公式addition law 加法定律addition law(of probability) （概率）加法定律additive inverse 加法逆元; 加法反元 additive property 可加性adjacent angle 邻角 adjacent side 邻边adjoint matrix 伴随矩阵algebra 代数 algebraic 代数的algebraic equation 代数方程 algebraic expression 代数式algebraic fraction 代数分式；代数分数式algebraic inequality 代数不等式algebraic number 代数数 algebraic operation 代数运算algebraically closed 代数封闭 algorithm 算法系统; 规则系统alternate angle （交）错角 alternate segment 内错弓形alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设altitude 高；高度；顶垂线；高线ambiguous case 两义情况；二义情况amount 本利和；总数 analysis 分析；解析analytic geometry 解析几何angle 角 angle at the centre 圆心角angle at the circumference 圆周角angle between a line and a plane 直与平面的交角angle between two planes 两平面的交角angle bisection 角平分angle bisector 角平分线；分角线angle in the alternate segment 交错弓形的圆周角angle in the same segment 同弓形内的圆周角angle of depression 俯角angle of elevation 仰角angle of friction 静摩擦角; 极限角angle of greatest slope 最大斜率的角angle of inclination 倾斜角angle of intersection 相交角；交角angle of projection 投射角angle of rotation 旋转角angle of the sector 扇形角 angle sum of a triangle 三角形内角和angles at a point 同顶角 angular displacement 角移位angular momentum 角动量 angular motion 角运动angular velocity 角速度annum(X% per annum) 年（年利率X%）anti-clockwise direction 逆时针方向；返时针方向anti-clockwise moment 逆时针力矩anti-derivative 反导数; 反微商anti-logarithm 逆对数；反对数anti-symmetric 反对称apex 顶点 approach 接近；趋近approximate value 近似值 approximation 近似；略计；逼近Arabic system 阿刺伯数字系统 arbitrary 任意arbitrary constant 任意常数 arc 弧arc length 弧长 arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积 Argand diagram 阿根图, 阿氏图argument (1)论证; (2)辐角argument of a complex number 复数的辐角argument of a function 函数的自变量arithmetic 算术arithmetic mean 算术平均；等差中顶；算术中顶arithmetic progression 算术级数；等差级数arithmetic sequence 等差序列arithmetic series 等差级数 arm 边array 数组; 数组arrow 前号 ascending order 递升序ascending powers of X X 的升幂 assertion 断语; 断定associative law 结合律 assumed mean 假定平均数assumption 假定；假设asymmetrical 非对称asymptote 渐近asymptotic error constant 渐近误差常数at rest 静止augmented matrix 增广矩阵auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 辅助方程average 平均；平均数；平均值average speed 平均速率axiom 公理axiom of existence 存在公理axiom of extension 延伸公理axiom of inclusion 包含公理axiom of pairing 配对公理axiom of power 幂集公理axiom of specification 分类公理axiomatic theory of probability 概率公理论axis 轴axis of parabola 拋物线的轴axis of revolution 旋转轴axis of rotation 旋转轴axis of symmetry 对称轴 back substitution 回代bar chart 棒形图；条线图；条形图；线条图 base （1）底；（2）基；基数base angle 底角 base area 底面base line 底线 base number 底数；基数base of logarithm 对数的底 basis 基Bayes´ theorem 贝叶斯定理bearing 方位（角）；角方向（角）bell-shaped curve 钟形图belong to 属于Bernoulli distribution 伯努利分布Bernoulli trials 伯努利试验bias 偏差；偏倚biconditional 双修件式; 双修件句bijection 对射; 双射; 单满射bijective function 对射函数; 只射函数billion 十亿bimodal distribution 双峰分布binary number 二进数binary operation 二元运算binary scale 二进法binary system 二进制binomial 二项式 binomial distribution 二项分布binomial expression 二项式 binomial series 二项级数binomial theorem 二项式定理 bisect 平分；等分bisection method 分半法；分半方法bisector 等分线；平分线Boolean algebra 布尔代数boundary condition 边界条件boundary line 界（线）；边界bounded 有界的bounded above 有上界的；上有界的bounded below 有下界的；下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号 bracket 括号breadth 阔度 broken line graph 折线图calculation 计算calculator 计算器；计算器calculus (1) 微积分学; (2) 演算 cancel 消法；相消canellation law 消去律 canonical 典型; 标准capacity 容量 cardioid 心脏Cartesian coordinates 笛卡儿坐标Cartesian equation 笛卡儿方程Cartesian plane 笛卡儿平面Cartesian product 笛卡儿积category 类型；范畴catenary 悬链Cauchy sequence 柯西序列Cauchy´s principal value 柯西主值Cauchy-Schwarz inequality 柯西 - 许瓦尔兹不等式central limit theorem 中心极限定理central line 中线central tendency 集中趋centre 中心；心centre of a circle 圆心centre of gravity 重心centre of mass 质量中心centrifugal force 离心力centripedal acceleration 向心加速度centripedal force force 向心力centroid 形心；距心certain event 必然事件chain rule 链式法则chance 机会change of axes 坐标轴的变换change of base 基的变换change of coordinates 坐标轴的变换change of subject 主项变换change of variable 换元；变量的换characteristic equation 特征(征)方程characteristic function 特征(征)函数characteristic of logarithm 对数的首数; 对数的定位部characteristic root 特征(征)根chart 图；图表check digit 检验数位checking 验算chord 弦chord of contact 切点弦circle 圆circular 圆形；圆的circular function 圆函数；三角函数circular measure 弧度法circular motion 圆周运动circular permutation 环形排列; 圆形排列; 循环排列circumcentre 外心；外接圆心circumcircle 外接圆circumference 圆周circumradius 外接圆半径circumscribed circle 外接圆cissoid 蔓叶class 区；组；类class boundary 组界class interval 组区间；组距class limit 组限；区限class mark 组中点；区中点classical theory of probability 古典概率论classification 分类clnometer 测斜仪clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coaxial 共轴coaxial circles 共轴圆coaxial system 共轴系coded data 编码数据coding method 编码法co-domain 上域coefficient 系数coefficient of friction 摩擦系数coefficient of restitution 碰撞系数; 恢复系数coefficient of variation 变差系数cofactor 余因子; 余因式cofactor matrix 列矩阵coincide 迭合；重合collection of terms 并项collinear 共线collinear planes 共线面collision 碰撞column (1)列；纵行；(2) 柱column matrix 列矩阵column vector 列向量combination 组合common chord 公弦common denominator 同分母；公分母common difference 公差common divisor 公约数；公约common factor 公因子；公因子common logarithm 常用对数common multiple 公位数；公倍common ratio 公比common tangent 公切commutative law 交换律comparable 可比较的compass 罗盘compass bearing 罗盘方位角compasses 圆规compasses construction 圆规作图compatible 可相容的complement 余；补余complement law 补余律complementary angle 余角complementary equation 补充方程complementary event 互补事件complementary function 余函数complementary probability 互补概率complete oscillation 全振动completing the square 配方complex conjugate 复共轭complex number 复数complex unmber plane 复数平面complex root 复数根component 分量component of force 分力composite function 复合函数; 合成函数composite number 复合数；合成数composition of mappings 映射构合composition of relations 复合关系compound angle 复角compound angle formula 复角公式compound bar chart 综合棒形图compound discount 复折扣compound interest 复利；复利息compound probability 合成概率compound statement 复合命题; 复合叙述computation 计算computer 计算机；电子计算器concave 凹concave downward 凹向下的concave polygon 凹多边形concave upward 凹向上的concentric circles 同心圆concept 概念conclusion 结论concurrent 共点concyclic 共圆concyclic points 共圆点condition 条件conditional 条件句；条件式conditional identity 条件恒等式conditional inequality 条件不等式conditional probability 条件概率cone 锥；圆锥（体）confidence coefficient 置信系数confidence interval 置信区间confidence level 置信水平confidence limit 置信极限confocal section 共焦圆锥曲congruence (1)全等；(2)同余congruence class 同余类congruent 全等congruent figures 全等图形congruent triangles 全等三角形conic 二次曲; 圆锥曲conic section 二次曲; 圆锥曲conical pendulum 圆锥摆conjecture 猜想conjugate 共轭conjugate axis 共轭conjugate diameters 共轭轴conjugate hyperbola 共轭(直)径conjugate imaginary / complex number 共轭双曲conjugate radical 共轭虚/复数conjugate surd 共轭根式; 共轭不尽根conjunction 合取connective 连词connector box 捙接框consecutive integers 连续整数consecutive numbers 连续数；相邻数consequence 结论；推论consequent 条件；后项conservation of energy 能量守恒conservation of momentum 动量守恒conserved 守恒consistency condition 相容条件consistent 一贯的；相容的consistent estimator 相容估计量constant 常数constant acceleration 恒加速度constant force 恒力constant of integration 积分常数constant speed 恒速率constant term 常项constant velocity 怛速度constraint 约束；约束条件construct 作construction 作图construction of equation 方程的设立continued proportion 连比例continued ratio 连比continuity 连续性continuity correction 连续校正continuous 连续的continuous data 连续数据continuous function 连续函数continuous proportion 连续比例continuous random variable 连续随机变量contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数converse 逆(定理)converse of a relation 逆关系converse theorem 逆定理conversion 转换convex 凸convex polygon 凸多边形convexity 凸性coordinate 坐标coordinate geometry 解析几何；坐标几何coordinate system 坐标系系定理；系；推论coplanar 共面coplanar forces 共面力coplanar lines 共面co-prime 互质; 互素corollary 系定理; 系; 推论correct to 准确至；取值至correlation 相关correlation coefficient 相关系数correspondence 对应corresponding angles (1)同位角；(2)对应角corresponding element 对应边corresponding sides 对应边cosecant 余割cosine 余弦cosine formula 余弦公式cost price 成本cotangent 余切countable 可数countable set 可数集countably infinite 可数无限counter clockwise direction 逆时针方向；返时针方向counter example 反例counting 数数；计数couple 力偶Carmer´s rule 克莱玛法则criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cross-multiplication 交叉相乘cross-section 横切面；横截面；截痕cube 正方体；立方；立方体cube root 立方根cubic 三次方；立方；三次(的)cubic equation 三次方程cubic roots of unity 单位的立方根cuboid 长方体；矩体cumulative 累积的cumulative distribution function 累积分布函数cumulative frequecy 累积频数；累积频率cumulative frequency curve 累积频数曲cumulative frequcncy distribution 累积频数分布cumulative frequency polygon 累积频数多边形；累积频率直方图curvature of a curve 曲线的曲率curve 曲线curve sketching 曲线描绘(法)curve tracing 曲线描迹(法)curved line 曲线curved surface 曲面curved surface area 曲面面积cyclic expression 输换式cyclic permutation 圆形排列cyclic quadrilateral 圆内接四边形cycloid 旋输线; 摆线cylinder 柱；圆柱体cylindrical 圆柱形的damped oscillation 阻尼振动data 数据De Moivre´s theorem 棣美弗定理De Morgan´s law 德摩根律decagon 十边形decay 衰变decay factor 衰变因子decelerate 减速decelaration 减速度decile 十分位数decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制decision box 判定框declarative sentence 说明语句declarative statement 说明命题decoding 译码decrease 递减decreasing function 递减函数；下降函数decreasing sequence 递减序列；下降序列decreasing series 递减级数；下降级数decrement 减量deduce 演绎deduction 推论deductive reasoning 演绎推理definite 确定的；定的definite integral 定积分definition 定义degenerated conic section 降级锥曲线degree (1) 度; (2) 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of confidence 置信度degree of freedom 自由度degree of ODE 常微分方程次数degree of precision 精确度delete 删除; 删去denary number 十进数denominator 分母dependence (1)相关; (2)应变dependent event(s) 相关事件; 相依事件; 从属事件dependent variable 应变量; 应变数depreciation 折旧derivable 可导derivative 导数derived curve 导函数曲线derived function 导函数derived statistics 推算统计资料; 派生统计资料descending order 递降序descending powers of x x的降序descriptive statistics 描述统计学detached coefficients 分离系数(法)determinant 行列式deviation 偏差; 变差deviation from the mean 离均差diagonal 对角线diagonal matrix 对角矩阵diagram 图; 图表diameter 直径diameter of a conic 二次曲线的直径difference 差difference equation 差分方程difference of sets 差集differentiable 可微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiate from first principle 从基本原理求导数differentiation 微分法digit 数字dimension 量; 量网; 维(数)direct impact 直接碰撞direct image 直接像direct proportion 正比例direct tax, direct taxation 直接税direct variation 正变(分)directed angle 有向角directed line 有向直线directed line segment 有向线段directed number 有向数direction 方向; 方位direction angle 方向角direction cosine 方向余弦direction number 方向数direction ratio 方向比directrix 准线Dirichlet function 狄利克来函数discontinuity 不连续性discontinuous 间断(的);连续(的); 不连续(的) discontinuous point 不连续点discount 折扣discrete 分立; 离散discrete data 离散数据; 间断数据discrete random variable 间断随机变数discrete uniform distribution 离散均匀分布discriminant 判别式disjoint 不相交的disjoint sets 不相交的集disjunction 析取dispersion 离差displacement 位移disprove 反证distance 距离distance formula 距离公式distinct roots 相异根distincr solution 相异解distribution 公布distributive law 分配律diverge 发散divergence 发散(性)divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divergent series 发散级数divide 除dividend (1)被除数；(2)股息divisible 可整除division 除法division algorithm 除法算式divisor 除数；除式；因子divisor of zero 零因子dodecagon 十二边形domain 定义域dot 点dot product 点积double angle 二倍角double angle formula 二倍角公式double root 二重根dual 对偶duality (1)对偶性; (2) 双重性due east/ south/ west /north 向东/ 南/ 西/ 北dynamics 动力学eccentric angle 离心角eccentric circles 离心圆eccentricity 离心率echelon form 梯阵式echelon matrix 梯矩阵edge 棱；边efficient estimator 有效估计量effort 施力eigenvalue 本征值eigenvector 本征向量elastic body 弹性体elastic collision 弹性碰撞elastic constant 弹性常数elastic force 弹力elasticity 弹性element 元素elementary event 基本事件elementary function 初等函数elementary row operation 基本行运算elimination 消法elimination method 消去法；消元法ellipse 椭圆ellipsiod 椭球体elliptic function 椭圆函数elongation 伸张；展empirical data 实验数据empirical formula 实验公式empirical probability 实验概率；经验概率empty set 空集encoding 编码enclosure 界限end point 端点energy 能; 能量entire surd 整方根epicycloid 外摆线equal 相等equal ratios theorem 等比定理equal roots 等根equal sets 等集equality 等(式)equality sign 等号equation 方程equation in one unknown 一元方程equation in two unknowns(variables) 二元方程equation of a straight line 直线方程equation of locus 轨迹方程equiangular 等角(的)equidistant 等距(的)equilateral 等边(的)equilateral polygon 等边多边形equilateral triangle 等边三角形equilibrium 平衡equiprobable 等概率的equiprobable space 等概率空间equivalence 等价equivalence class 等价类equivalence relation 等价关系equivalent 等价(的)error 误差error allowance 误差宽容度error estimate 误差估计error term 误差项error tolerance 误差宽容度escribed circle 旁切圆estimate 估计；估计量estimator 估计量Euclidean algorithm 欧几里德算法Euclidean geometry 欧几里德几何Euler´s formula 尤拉公式；欧拉公式evaluate 计值even function 偶函数even number 偶数evenly distributed 均匀分布的event 事件exact 真确exact differential form 恰当微分形式exact solution 准确解；精确解；真确解exact value 法确解；精确解；真确解example 例excentre 外心exception 例外excess 起exclusive 不包含exclusive disjunction 不包含性析取exclusive events 互斥事件exercise 练习exhaustive event(s) 彻底事件existential quantifier 存在量词expand 展开expand form 展开式expansion 展式expectation 期望expectation value, expected value 期望值；预期值experiment 实验；试验experimental 试验的experimental probability 实验概率explicit function 显函数exponent 指数exponential function 指数函数exponential order 指数阶; 指数级express…in terms of… 以………表达expression 式；数式extension 外延；延长；扩张；扩充v1.0 可编辑可修改extension of a function 函数的扩张exterior angle 外角external angle bisector 外分角external point of division 外分点extreme point 极值点extreme value 极值extremum 极值face 面factor 因子；因式；商factor method 因式分解法factor theorem 因子定理；因式定理factorial 阶乘factorization 因子分解；因式分解factorization of polynomial 多项式因式分解fallacy 谬误FALSE 假(的)falsehood 假值family 族family of circles 圆族family of concentric circles 同心圆族family of straight lines 直线族feasible solution 可行解；容许解Fermat´s last theorem 费尔马最后定理Fibonacci number 斐波那契数；黄金分割数Fibonacci sequence 斐波那契序列fictitious mean 假定平均数figure (1)图(形)；(2)数字final velocity 末速度finite 有限finite dimensional vector space 有限维向量空间finite population 有限总体finite probability space 有限概率空间finite sequence 有限序列finite series 有限级数finite set 有限集first approximation 首近似值first derivative 一阶导数first order differential equation 一阶微分方程first projection 第一投影; 第一射影first quartile 第一四分位数first term 首项fixed deposit 定期存款fixed point 定点fixed point iteration method 定点迭代法fixed pulley 定滑轮flow chart 流程图focal axis 焦轴focal chord 焦弦focal length 焦距focus(foci) 焦点folium of Descartes 笛卡儿叶形线foot of perpendicular 垂足for all X 对所有Xfor each /every X 对每一Xforce 力forced oscillation 受迫振动form 形式；型formal proof 形式化的证明format 格式；规格formula(formulae) 公式four leaved rose curve 四瓣玫瑰线four rules 四则four-figure table 四位数表fourth root 四次方根fraction 分数；分式fraction in lowest term 最简分数fractional equation 分式方程fractional index 分数指数fractional inequality 分式不等式free fall 自由下坠free vector 自由向量; 自由矢量frequency 频数；频率frequency distribution 频数分布；频率分布frequency distribution table 频数分布表frequency polygon 频数多边形；频率多边形friction 摩擦; 摩擦力frictionless motion 无摩擦运动frustum 平截头体fulcrum 支点function 函数function of function 复合函数；迭函数functional notation 函数记号fundamental theorem of algebra 代数基本定理fundamental theorem of calculus 微积分基本定理gain 增益；赚；盈利gain perent 赚率；增益率；盈利百分率game （1）对策；（2）博奕Gaussian distribution 高斯分布Gaussian elimination 高斯消去法general form 一般式；通式general solution 通解；一般解general term 通项generating function 母函数; 生成函数generator (1)母线; (2)生成元geoborad 几何板geometric distribution 几何分布geometric mean 几何平均数；等比中项geometric progression 几何级数；等比级数geometric sequence 等比序列geometric series 等比级数geometry 几何；几何学given 给定；已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值golden section 黄金分割grade 等级gradient (1)斜率；倾斜率；(2)梯度grand total 总计graph 图像；图形；图表graph paper 图表纸graphical method 图解法graphical representation 图示；以图样表达graphical solution 图解gravitational acceleration 重力加速度gravity 重力greatest term 最大项greatest value 最大值grid lines 网网格线group 组；grouped data 分组数据；分类数据grouping terms 并项；集项growth 增长growth factor 增长因子half angle 半角half angle formula 半角公式half closed interval 半闭区间half open interval 半开区间harmonic mean (1) 调和平均数; (2) 调和中项harmonic progression 调和级数head 正面（钱币）height 高（度）helix 螺旋线hemisphere 半球体；半球heptagon 七边形Heron´s formula 希罗公式heterogeneous (1)参差的; (2)不纯一的hexagon 六边形higher order derivative 高阶导数highest common factor 最大公因子；最高公因式；最高公因子Hindu-Arabic numeral 阿刺伯数字histogram 组织图；直方图；矩形图Holder´s Inequality 赫耳德不等式homogeneous 齐次的homogeneous equation 齐次方程Hooke´s law 虎克定律horizontal 水平的；水平horizontal asymptote 水平渐近线horizontal component 水平分量horizontal line 横线；水平线horizontal range 水平射程hyperbola 双曲线hyperbolic function 双曲函数hypergeometric distribution 超几何分布hypocycloid 内摆线hypotenuse 斜边hypothesis 假设hypothesis testing 假设检验hypothetical syllogism 假设三段论hypotrochoid 次内摆线idempotent 全幂等的identical 全等；恒等identity 等（式）identity element 单位元identity law 同一律identity mapping 恒等映射identity matrix 恒等矩阵identity relation 恒等关系式if and only if/iff 当且仅当；若且仅若if…, then 若….则；如果…..则illustration 例证；说明image 像点；像image axis 虚轴imaginary circle 虚圆imaginary number 虚数imaginary part 虚部imaginary root 虚根imaginary unit 虚数单位impact 碰撞implication 蕴涵式；蕴含式implicit definition 隐定义implicit function 隐函数imply 蕴涵；蕴含impossible event 不可能事件improper fraction 假分数improper integral 广义积分; 非正常积分impulse 冲量impulsive force 冲力incentre 内力incircle 内切圆inclination 倾角；斜角inclined plane 斜面included angle 夹角included side 夹边inclusion mapping 包含映射inclusive 包含的；可兼的inclusive disjunction 包含性析取；可兼析取inconsistent 不相的(的)；不一致(的) increase 递增；增加increasing function 递增函数increasing sequence 递增序列increasing series 递增级数increment 增量indefinite integral 不定积分idenfinite integration 不定积分法independence 独立；自变independent equations 独立方程independent event 独立事件independent variable 自变量；独立变量indeterminate (1)不定的；(2)不定元；未定元indeterminate coefficient 不定系数；未定系数indeterminate form 待定型；不定型index,indices 指数；指index notation 指数记数法induced operation 诱导运算induction hypothesis 归纳法假设inelastic collision 非弹性碰撞inequality 不等式；不等inequality sign 不等号inertia 惯性；惯量infer 推断inference 推论infinite 无限；无穷infinite dimensional 无限维infinite population 无限总体infinite sequence 无限序列；无穷序列infinite series 无限级数；无穷级数infinitely many 无穷多infinitesimal 无限小；无穷小infinity 无限(大)；无穷(大)inflection (inflexion) point 拐点；转折点inherent error 固有误差initial approximation 初始近似值initial condition 原始条件；初值条件initial point 始点；起点initial side 始边initial value 初值；始值initial velocity 初速度initial-value problem 初值问题injection 内射injective function 内射函数inner product 内积input 输入input box 输入inscribed circle 内切圆insertion 插入insertion of brackets 加括号instantaneous 瞬时的instantaneous acceleration 瞬时加速度instantaneous speed 瞬时速率instantaneous velocity 瞬时速度integer 整数integrable 可积integrable function 可积函数integral 积分integral index 整数指数integral mean value theorem 积数指数integral part 整数部份integral solution 整数解integral value 整数值integrand 被积函数integrate 积；积分；......的积分integrating factor 积分因子integration 积分法integration by parts 分部积分法integration by substitution 代换积分法；换元积分法integration constant 积分常数interaction 相互作用intercept 截距；截段intercept form 截距式v1.0 可编辑可修改intercept theorem 截线定理interchange 互换interest 利息interest rate 利率interest tax 利息税interior angle 内角interior angles on the same side of the transversal 同旁内角interior opposite angle 内对角intermediate value theorem 介值定理internal bisector 内分角internal division 内分割internal energy 内能internal force 内力internal point of division 内分点interpolating polynomial 插值多项式interpolation 插值inter-quartile range 四分位数间距intersect 相交intersection (1)交集；(2)相交；(3)交点interval 区间interval estimation 区间估计；区域估计intuition 直观invalid 失效；无效invariance 不变性invariant (1)不变的；(2)不变量；不变式inverse 反的；逆的inverse circular function 反三角函数inverse cosine function 反余弦函数inverse function 反函数；逆函数inverse cosine function 反三角函数inverse function 反函数；逆映射inverse mapping 反向映射；逆映射inverse matrix 逆矩阵inverse problem 逆算问题inverse proportion 反比例；逆比例inverse relation 逆关系inverse sine function 反正弦函数inverse tangent function 反正切函数inverse variation 反变(分)；逆变(分) invertible 可逆的invertible matrix 可逆矩阵irrational equation 无理方程irrational number 无理数irreducibility 不可约性irregular 不规则isomorphism 同构isosceles triangle 等腰三角形iterate (1)迭代值; (2)迭代iteration 迭代iteration form 迭代形iterative function 迭代函数iterative method 迭代法jet propulsion 喷气推进joint variation 联变(分)；连变(分)kinetic energy 动能kinetic friction 动摩擦known 己知末项L´Hospital´s rule 洛必达法则Lagrange interpolating polynomial 拉格朗日插值多项代Lagrange theorem 拉格朗日定理Lami´s law 拉密定律Laplace expansion 拉普拉斯展式last term 末项latent root 本征根; 首通径lattice point 格点latus rectum 正焦弦; 首通径law 律；定律law of conservation of momentum 动量守恒定律law of indices 指数律；指数定律law of inference 推论律law of trichotomy 三分律leading coefficient 首项系数leading diagonal 主对角线least common multiple, lowest common multiple 最小公倍数；最低公倍式least value 最小值left hand limit 左方极限lemma 引理lemniscate 双纽线length 长(度)letter 文字；字母v1.0 可编辑可修改like surd 同类根式like terms 同类项limacon 蜗牛线limit 极限limit of sequence 序列的极限limiting case 极限情况limiting friction 最大静摩擦limiting position 极限位置line 线；行line of action 作用力线line of best-fit 最佳拟合line of greatest slope 最大斜率的直；最大斜率line of intersection 交线line segment 线段linear 线性；一次linear convergence 线性收敛性linear differeantial equation 线性微分方程linear equation 线性方程；一次方程linear equation in two unknowns 二元一次方程；二元线性方程linear inequality 一次不等式；线性不等式linear momentum 线动量linear programming 线性规划linearly dependent 线性相关的linearly independent 线性无关的literal coefficient 文字系数literal equation 文字方程load 负荷loaded coin 不公正钱币loaded die 不公正骰子local maximum 局部极大(值)local minimum 局部极小(值)locus, loci 轨迹logarithm 对数logarithmic equation 对数方程logarithmic function 对数函数logic 逻辑logical deduction 逻辑推论；逻辑推理logical step 逻辑步骤long division method 长除法loop 回路loss 赔本；亏蚀loss per cent 赔率；亏蚀百分率lower bound 下界lower limit 下限lower quartile 下四分位数lower sum 下和lower triangular matrix 下三角形矩阵lowest common multiple 最小公倍数machine 机械Maclaurin expansion 麦克劳林展开式Maclaurin series 麦克劳林级数magnitude 量；数量；长度；大小major arc 优弧；大弧major axis 长轴major sector 优扇形；大扇形major segment 优弓形；大弓形mantissa 尾数mantissa of logarithm 对数的尾数；对数的定值部many to one 多个对一个many-sided figure 多边形many-valued 多值的map into 映入map onto 映上mapping 映射marked price 标价Markov chain 马可夫链mass 质量mathematical analysis 数学分析mathematical induction 数学归纳法mathematical sentence 数句mathematics 数学matrix 阵; 矩阵matrix addition 矩阵加法matrix equation 矩阵方程matrix multiplication 矩阵乘法matrix operation 矩阵运算maximize 极大maximum absolute error 最大绝对误差maximum point 极大点maximum value 极大值mean 平均(值)；平均数；中数v1.0 可编辑可修改mean deviation 中均差；平均偏差mean value theorem 中值定理measure of dispersion 离差的量度measurement 量度mechanical energy 机械能median (1)中位数；(2)中线meet 相交；相遇mensuration 计量；求积法method 方法method of completing square 配方法method of interpolation 插值法; 内插法method of least squares 最小二乘法; 最小平方法method of substitution 代换法；换元法method of successive substitution 逐次代换法; 逐次调替法method of superposition 迭合法metric unit 十进制单位mid-point 中点mid-point formula 中点公式mid-point theorem 中点定理million 百万minimize 极小minimum point 极小点minimum value 极小值Minkowski Inequality 闵可夫斯基不等式minor (1)子行列式；(2)劣；较小的minor arc 劣弧；小弧minor axis 短轴minor of a determinant 子行列式minor sector 劣扇形；小扇形minor segment 劣弓形；小弓形minus 减minute 分mixed number(fraction) 带分数modal class 众数组mode 众数model 模型modulo (1)模; 模数; (2)同余modulo arithmetic 同余算术modulus 模; 模数modulus of a complex number 复数的模modulus of elasticity 弹性模(数)moment arm (1)矩臂; (2)力臂moment of a force 力矩moment of inertia 贯性矩momentum 动量monomial 单项式monotone 单调monotonic convergence 单调收敛性monotonic decreasing 单调递减monotonic decreasing function 单调递减函数monotonic function 单调函数monotonic increasing 单调递增monotonic increasing function 单调递增函数motion 运动movable pulley 动滑轮multinomial 多项式multiple 倍数multiple angle 倍角multiple-angle formula 倍角公式multiple root 多重根multiplicand 被乘数multiplication 乘法multiplication law (of probability) (概率)乘法定律multiplicative inverse 乘法逆元multiplicative property 可乘性multiplicity 重数multiplier 乘数；乘式multiply 乘multi-value 多值的mulually disjoint 互不相交mutually exclusive events 互斥事件mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直n factorial n阶乘n th derivative n阶导数n th root n次根；n次方根n the root of unity 单位的n次根Napierian logarithm 纳皮尔对数; 自然对数natural logarithm 自然对数natural number 自然数natural surjection 自然满射。

IndexEEconomics 经济学435,439 Eigencourse 457,458Eigenvalue 特征值283,287,374,499 Eigenvalue changes 特征值变换439Eigenvalues of 的特征值284,294,300 Eigenvalues of 的特征值297Eigenvalues of 的特征值362Eigenvector basis 基底的特征向量399Eigenvectors 特征向量283,287,374Eigshow 290,368Elimination 消元法45-66,83,86,135 Ellipse 椭圆290,346,366,382 Energy 能量343,409Engineering 工程409,419Error 误差211,218,219,225,481,483 Error equation 误差方程477Euler angles 欧拉角474Euler’s formula 欧拉公式311,426,430,497Even 偶数113,246,258,452 Exponential 指数的314,319,327FHilbert space 希尔伯特空间447,449Hooke’s Law 虎克定律410,412 Householder reflections 镜像变换237,469,472 Hyperplane 超平面30,42IIll-conditioned matrix 病态矩阵371,473,474 Imaginary 虚数289Independent 独立的26,27,134,168,200,300 Initial value 初值313Inner product 内积11,56,108,448,502,506 Input and output basis 基底输入输出399Integral 积分24,385,386Interior point method 内点法445Intersection of spaces 交空间129,183Inverse matrix 逆矩阵24,81,270Inverse of的逆82Invertible 可逆的86,173,200,248 Iteration 迭代481,482,484,489,492 JJacobi 雅可比481,483,485,489 Jordan form 约当型356,357,358,361,482 JPEG 364,373KKalman filter 卡尔曼滤波器93,214Kernel 核377,380Kirchhoff’s Laws 基尔霍夫定律143,189,420,424-427 Krylov 克雷洛夫491,492Lnorm 和范数225,480Lagrange multiplier 拉格朗日乘子445Lanczos method 兰索斯方法490,492LAPACK 线性代数软件包98,237,486Leapfrog method 跳步法317,329Least squares 最小平方218,219,236,405,408,453 Left nullspace左零空间184,186,192,425Left-inverse 左逆的81,86,154,405Length 长度12,232,447,448,501 Line 线34,40,221,474Line of springs 线弹簧411Linear combination 线性组合1,3Linear equation 线性方程23Linear programming 线性规划440Linear transformation 线性变换44,375-398Linearity 线性关系44,245,246Linearly independent 线性独立26,134,168,169,200 LINPACK 线性系统软件包465Loop 环路307,425,426Lower triangular 下三角9598,100,474Lucas numbers 卢卡斯数306MMaple 38,100Mathematica 38,100MATLAB 17,37,237,243,290,337,513 Matrix(see full page 570) 矩阵22,384,387Matrix exponential 矩阵指数314,319,327Matrix multiplication 矩阵乘法58,59,67,389Matrix notation 矩阵记号37Matrix space 矩阵空间121,122,175,181,311 Matrix 矩阵-1,2,-1 matrix -1，2，-1矩阵106,167,261,265,349,374,410,480Adjacency, 邻接矩阵74,80,311,369All-ones 全1矩阵251,262,307,348 Augmented 增广矩阵60,84,155Band 带状矩阵99,468,469。

Chapter 6 Eigenvalues1.Evaluate the eigenvalues and eigenvectors of the following matrices:（1）311201112A -⎡⎤⎢⎥=⎢⎥⎢⎥-⎣⎦（2）220212020A -⎡⎤⎢⎥=--⎢⎥⎢⎥-⎣⎦2. Let A be a 33⨯ matrix ，and matrices 2I A I A A I -+-、、are all singular 。

Then calculate ：（1）the eigenvalues of matrix A 。

（2）If matrix B is similar to matrix A ，then compute B 。

3. If 0λ is the eigenvalue of matrix A ，prove that 0k λ is an eigenvalue of matrix k A ，where k is integer 。

4.Suppose 0λ is an eigenvalue of matrix A ，()f x is a polynomial of x ，prove 0()f λ is the eigenvalue of ()f A 。

5. If matrix A is nonsingular ，prove that any eigenvalue 0λ of A is nonzero ，and10λ- is aneigenvalue of 1A -。

6. If 1，2，-3. are the eigenvalues of matrix A（1）Prove ：matrix A is nonsingular ，and calculate the eigenvalue of matrix 1A A -；（2）Compute the eigenvalue of matrix 223A I -。