线性代数常用单词词组中英对照

1、IndexAAddition of vectors向量的加法2,3,33,121All combinations所有组合5,122,123Angle between vectors向量间的夹角14,15Anti-symmetric(see Skew-symmetric)反对称109Area面积272,273,280Arnoldi iterationArnoldi迭代488,491,492Arrow箭头3,4,423Associative law结合律58,59,69,80Average平均值227,450,456BBack substitution回代45,49,98Backslash反斜杠9

2、9,156Basis基底168,172,180,200,391Big formula256,258Big picture187,199,421Binomial二项式442,454Bioinformatics生物信息学457BLAS:Basic Linear Algebra Subrontines基本线性代数子程序466Block elimination分块消去71Block multiplication分块相乘70,79Block pivot主元块94Boundary condition边界条件417Bowl353Box273,276CCalculus微积分学25,281,417Cauchy-

3、Binet282Cayley-Hamilton凯莱-哈密顿310,311,362Centered difference中心差分25,28,316,328Change of basis基底的变化358,390,391,396,400Characteristic polynomial特征多项式287Cholesky factorization柯勒斯基分解102,345,353,564Circle圆，圆周315,316Clock钟9Closest line最邻近线218,219,222Cofactors代数余子式255,259,260,265,270Column at a time逐列23,32,3

4、6Column picture列图32,34,40Column space C(A)列空间C(A)123,124,130Column vector列向量2,4Columns times rows列乘行62,68,71,145,150Combination of columns列的组合32,33,56Commutative交换的59,69Commuting matrices交换矩阵305Complete solution通解136,156,159,162,313Complex复数120,340,493,494,499,506,509Complex eigenvalues复特征值289,333Co

5、mplex eigenvectors复特征向量289,333Compression压缩364,373,391,410Computational science计算科学189,317,419,427Computer graphics电脑图形图像459,462,463Condition number条件数371,477,478Conjugate共轭的333,338,494,501,506Conjugate gradients共轭梯度486,492Constant coefficients常系数312Convolution卷积515Corner棱角8,441,443Cosine of angle余弦

6、角15,17,447Cosine Law余弦定律20Cosine of matrix余弦矩阵329Cost vector费用向量440Covariance协方差228,453-458Cramers Rule克拉默法则259,269,279Cross product叉积275,276Cube立方，立方体8,73,274,281,464Cyclic周期性的25,93,374DDelta functionDelta函数449,452Dependent相关的26,27,169,170Derivative导数24,109,229,384,395Determinant行列式63,244-280,288,2

7、95Diagonalizable可对角化300,304,308,334,335Diagonalization对角化298,300,330,332,363,399Differential equation微分方程312-329,416Dimension维数145,168,174,175,176,183,185,187Discrete cosines离散cosine336,373Discrete sines离散sine336,373Distance to subspace到子空间的距离212Distributive law分配律69Dot product点积11,56,108,447,502Dua

8、l problem对偶问题442,446EEconomics经济学435,439Eigencourse457,458Eigenvalue特征值283,287,374,499Eigenvalue changes特征值变换439Eigenvalues of 的特征值284,294,300Eigenvalues 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283,287,374Eigshow290,368Elimination消元法45-66,83,86,135Ellipse椭圆290,346,

9、366,382Energy能量343,409Engineering工程409,419Error误差211,218,219,225,481,483Error equation误差方程477Euler angles欧拉角474Eulers formula欧拉公式311,426,430,497Even偶数113,246,258,452Exponential指数的314,319,327FFactorization因式分解95,110,235,348,370,374False proof假证明305,338Fast Fourier Transform快速傅立叶变换393,493,511,565Feasi

10、ble set可行集440,441FFT(see Fast Fourier Transform)见快速傅里叶变换509-514Fibonacci菲波那契75,266,268,301,302,306,308Finite difference有限差分315-317,417Finite elements有限元412,419First-order system一阶方程组315,326Fixed-free固定-自由410,414,417,419Force balance平衡力412FORTRAN16,38Forward difference前向差分30Four Fundamental Subspaces

11、四个基本子空间184-199,368,424,507Fourier series傅立叶序列233,448,450,452Fourier Transform傅立叶变换393,509-514Fredholm Alternative弗雷德霍姆择一203Free自由133,135,137,144,146,155Full column rank列满秩157,170,405Full row rank行满秩159,405Function space函数空间121,448,449Fundamental Theorem of Linear Algebra (see Four Fundamental Subspa

12、ces)线性代数基本定理188,198,368GGaussian elimination高斯消元法45,49,135Gaussian probability distribution高斯概率分布455Gauss-Jordan高斯-约当83,84,91,469Gauss-Seidel高斯-塞德尔481,484,485,489Gene expression data基因表达数据457Geometric series等比数列436Gershgorin circles格尔什戈林圆491Gibbs phenomenon吉布斯效应451Givens rotation吉文斯旋转471Google谷歌368,

13、369,434Gram-Schmidt格拉姆-施密特223,234,236,241,370,469Graph图表74,143,307,311,420,422,423Group群119,354HHalf-plane半平面7Heat equation热方程式322,323Heisenberg海森堡305,310Hilbert space希尔伯特空间447,449Hookes Law虎克定律410,412Householder reflections镜像变换237,469,472Hyperplane超平面30,42I Ill-conditioned matrix病态矩阵371,473,474Imag

14、inary虚数289Independent独立的26,27,134,168,200,300Initial value初值313Inner product内积11,56,108,448,502,506Input 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86,173,200,248Iteration迭代481,482,484,4

15、89,492JJacobi雅可比481,483,485,489Jordan form约当型356,357,358,361,482JPEG364,373KKalman filter卡尔曼滤波器93,214Kernel核377,380Kirchhoffs Laws基尔霍夫定律143,189,420,424-427Krylov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 squar

16、es最小平方218,219,236,405,408,453Left nullspace左零空间184,186,192,425Left-inverse左逆的81,86,154,405Length长度12,232,447,448,501Line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44,245,246 Linearly indepe

17、ndent线性独立26,134,168,169,200LINPACK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306MMaple38,100Mathematica38,100MATLAB17,37,237,243,290,337,513Matrix(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37

18、Matrix space矩阵空间121,122,175,181,311Matrix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251,262,307,348Augmented增广矩阵60,84,155Band带状矩阵99,468,469Block分块矩阵70,94,115,266,348Circulant循环矩阵507,515Coefficient系数矩阵33,36Cofactor matrix伴随矩阵270Companion友矩阵295,322C

19、omplex matrix复矩阵339,499Consumption消费矩阵435,436Covariance协方差阵228,453,455,456,458Cyclic循环矩阵25,93,374Derivative导数矩阵385Difference差矩阵22,87,412Echelon梯矩阵137,143Eigenvalue matrix特征值矩阵298Eigenvector matrix特征向量矩阵298Elimination消元矩阵57,63,149Exponential指数矩阵314,319,327First difference一阶差分矩阵22,373Fourier傅里叶矩阵394,4

20、93,505,510,511Hadamard阿达马矩阵238,280Hermitian埃尔米特矩阵339,340,501,503,506,507Hessenberg黑森伯格矩阵262,488,492Hilbert希尔伯特矩阵92,254,348House宅矩阵378,382Hypercube超立方矩阵73Identity单位矩阵37,42,57,390Incidence关联矩阵420,422,429Indefinite不定矩阵343Inverse逆矩阵24,81,270Invertible可逆矩阵27,83,86,112,408,574Jacobian雅可比矩阵274Jordan若尔当矩阵35

21、6,358,462,565Laplacian( Graph Laplacian)（图）拉普拉斯矩阵428Leslie莱斯利矩阵435,439Magic奇幻矩阵43Markov马尔可夫矩阵43,285,294,369,373,431,437Negative definite负定矩阵343Nondiagonalizable不可对角化矩阵299,304,309Normal正规矩阵341,508,565Northwest西北矩阵119Nullspace matrix零空间矩阵136,147Orthogonal正交矩阵231,252,289Pascal帕斯卡矩阵66,72,88,101,348,359P

22、ermutation置换矩阵59,111,116,183,297Pivot matrix主矩阵97,104Population人口矩阵435Positive matrix正矩阵413,431,434,436Positive definite正定矩阵343,344,351,409,475Projection投影矩阵206,208,210,233,285,388,462,463Pseudoinverse伪逆矩阵199,399,403,404,565Rank-one秩1矩阵145,152,294,311,363Reflection反射矩阵243,286,336,469,471Rotation旋转矩阵

23、231,289,460,471Saddle-point鞍点矩阵115,343Second derivative (Hessian)二阶导数（黑塞）矩阵349,353Second difference (1,-2,1)二阶差分（1，-2，1）矩阵322,373,417Semidefinite半定矩阵345,415Shearing剪切矩阵379Similar相似矩阵355-362,400Sine matrix正弦矩阵349,354,373Singular奇异矩阵27,416,574Skew-symmetric反称矩阵289,320,327,338,341Sparse稀疏矩阵100,470,474,

24、465Stable, 稳定矩阵318Stiffness刚性矩阵317,409,412,419Stoichiometric化学计量矩阵430Sudoku数独矩阵44Sum matrix和矩阵24,87,271Symmetric对称矩阵109,330-341Translation平移矩阵459,463Triangular三角形矩阵95,236,247,271,289,335Tridiagonal三对角矩阵85,100,265,413,468,491Unitary酉矩阵504,505,506,510Vandermonde范德蒙德矩阵226,253,266,511Wavelet小波矩阵242Mean均

25、值228,453-457Minimum极小值349Multigrid多重网格485Multiplication by columns按列相乘23,36Multiplication by rows按行相乘36Multiplication count相乘次数68,80,99,467,469Multiplicity重数304,358Multiplier乘子45,46,50,96Nchoose选442,454-dimensional space维空间1,120netlib100Network网络420,427Newtons method牛顿法445No solution无解26,39,46,192No

26、ndiagonalizable不可对角化304,309Norm范数12,475,476,479,480,489Normal distribution正态分布455Normal equation正规方程210,211,453Normal matrix正规矩阵341,508,565Nullspace零空间132,185OOdd permutation奇置换113Ohms Law欧姆定律426Orthogonality正交性14,195,448Orthogonal complement正交补197,198,200Orthogonal spaces正交空间197Orthogonal subspaces

27、正交子空间195,196,204Orthogonal vectors正交向量14,195Orthonormal规范正交的230,234,240,504Orthonormal basis规范正交基367,368,449Orthonormal eigenvectors规范正交特征向量203,307,330,332,339,341,503PParabola抛物线224Parallelogram平行四边形3,8,272,383Partial pivoting部分主元消元（法）113,466,467Particular solution特解155,156,159Permutation置换44,47,23

28、1,257Perpendicular(see Orthogonality)垂直12,14Perpendicular eigenvectors垂直特征向量203,339Perron-Frobenius Theorem佩龙-弗罗贝尼乌斯定理434Pivcol,主列146Pivot主元45,46,55,256,333,351,466Pivot columns主列133,135,138,144,146,173,185Pivot rows主行185Pivot variable主变元135,155Pixel,像素364,462Plane平面6,26Plane rotation,平面旋转471Poisson

29、 distribution,泊松分布454Polar coordinates极坐标274,281,495-497Polar decomposition极分解402,403Positive eigenvalues正特征值342Positive pivots正主元343Potential位势423Power method（乘）幂法487Preconditioner预调节器481,486Principal axes主轴330Principal Component Analysis主成分分析457Probability概率432,453,454Product of pivots主元的积63,85,24

30、4,333Projection投影206-217,219,233Projection on line线上投影207,208Projection on subspace子空间上投影209,210Projective space射影空间460Pseudoniverse伪逆199,399,403,404,407Pythagoras毕达哥拉斯14,20PYTHON16,100Qfactorization分解243,564method方法360,487,490RRandom随机21,55,348,373,562Range值域，区域376,377,380Rank秩144,159,160,166Rank o

31、f的秩153,194,217Rank one秩1145,150,152,189Rayleigh quotientRayleigh商476Real eigenvalues实特征值330,331Recursion递归，递推213,228,260,392,513Reduced cost缩减费用443,444Reduced echelon form(rref)缩减梯形式85,134,138,148, 166,564Reflection镜射（反射）232,243,286,336,471Regression回归453Repeated eigenvalues重特征值299,320,322Residual剩余

32、（的）；残差222,481,492Reverse order逆序82,107Right angle(see Orthogonality)直角14Right hand rule右手定则276Right-inverse右逆81,86,154,405Rotation旋转2321,289,460,471,474Roundoff error舍入误差371,466,477,478Row exchange行交换47,59,113,245,253Row picture行图31,34,40Row reduced echelon form行缩减梯形式85Row space 行空间171,184SSaddle鞍点3

33、53Scalar标量2,32Schur complementSchur补72,94,348Schurs TheoremSchur定理335,341Schwarz inequality施瓦茨不等式16,20,447Search engine搜索引擎373Second difference二阶差分316,322,336Second order equation二阶方程314-317Shake a Stick474Shift移位375Sigma notation56Simplex method单纯形法440,443Singular value奇异值363,365,371,476Singular Value Decomposition, see SVD奇异值分解Singular vector奇异向量363,408Skew-symmetric反对称289,320,327,338,3