線性代數(shù)常用單詞詞組中英對照

1、IndexAAddition of vectors向量的加法2,3,33,121All combinations所有組合5,122,123Angle between vectors向量間的夾角14,15Anti-symmetric(see Skew-symmetric)反對稱109Area面積272,273,280Arnoldi iterationArnoldi迭代488,491,492Arrow箭頭3,4,423Associative law結(jié)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二項(xiàng)式442,454Bioinformatics生物信息學(xué)457BLAS:Basic Linear Algebra Subrontines基本線性代數(shù)子程序466Block elimination分塊消去71Block multiplication分塊相乘70,79Block pivot主元塊94Boundary condition邊界條件417Bowl353Box273,276CCalculus微積分學(xué)25,281,417Cauchy-

3、Binet282Cayley-Hamilton凱萊-哈密頓310,311,362Centered difference中心差分25,28,316,328Change of basis基底的變化358,390,391,396,400Characteristic polynomial特征多項(xiàng)式287Cholesky factorization柯勒斯基分解102,345,353,564Circle圓，圓周315,316Clock鐘9Closest line最鄰近線218,219,222Cofactors代數(shù)余子式255,259,260,265,270Column at a time逐列23,32,3

4、6Column picture列圖32,34,40Column space C(A)列空間C(A)123,124,130Column vector列向量2,4Columns times rows列乘行62,68,71,145,150Combination of columns列的組合32,33,56Commutative交換的59,69Commuting matrices交換矩陣305Complete solution通解136,156,159,162,313Complex復(fù)數(shù)120,340,493,494,499,506,509Complex eigenvalues復(fù)特征值289,333Co

5、mplex eigenvectors復(fù)特征向量289,333Compression壓縮364,373,391,410Computational science計(jì)算科學(xué)189,317,419,427Computer graphics電腦圖形圖像459,462,463Condition number條件數(shù)371,477,478Conjugate共軛的333,338,494,501,506Conjugate gradients共軛梯度486,492Constant coefficients常系數(shù)312Convolution卷積515Corner棱角8,441,443Cosine of angle余弦

6、角15,17,447Cosine Law余弦定律20Cosine of matrix余弦矩陣329Cost vector費(fèi)用向量440Covariance協(xié)方差228,453-458Cramers Rule克拉默法則259,269,279Cross product叉積275,276Cube立方，立方體8,73,274,281,464Cyclic周期性的25,93,374DDelta functionDelta函數(shù)449,452Dependent相關(guān)的26,27,169,170Derivative導(dǎo)數(shù)24,109,229,384,395Determinant行列式63,244-280,288,2

7、95Diagonalizable可對角化300,304,308,334,335Diagonalization對角化298,300,330,332,363,399Differential equation微分方程312-329,416Dimension維數(shù)145,168,174,175,176,183,185,187Discrete cosines離散cosine336,373Discrete sines離散sine336,373Distance to subspace到子空間的距離212Distributive law分配律69Dot product點(diǎn)積11,56,108,447,502Dua

8、l problem對偶問題442,446EEconomics經(jīng)濟(jì)學(xué)435,439Eigencourse457,458Eigenvalue特征值283,287,374,499Eigenvalue changes特征值變換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橢圓290,346,

9、366,382Energy能量343,409Engineering工程409,419Error誤差211,218,219,225,481,483Error equation誤差方程477Euler angles歐拉角474Eulers formula歐拉公式311,426,430,497Even偶數(shù)113,246,258,452Exponential指數(shù)的314,319,327FFactorization因式分解95,110,235,348,370,374False proof假證明305,338Fast Fourier Transform快速傅立葉變換393,493,511,565Feasi

10、ble set可行集440,441FFT(see Fast Fourier Transform)見快速傅里葉變換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一階方程組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、四個(gè)基本子空間184-199,368,424,507Fourier series傅立葉序列233,448,450,452Fourier Transform傅立葉變換393,509-514Fredholm Alternative弗雷德霍姆擇一203Free自由133,135,137,144,146,155Full column rank列滿秩157,170,405Full row rank行滿秩159,405Function space函數(shù)空間121,448,449Fundamental Theorem of Linear Algebra (see Four Fundamental Subspa

12、ces)線性代數(shù)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-約當(dāng)83,84,91,469Gauss-Seidel高斯-塞德爾481,484,485,489Gene expression data基因表達(dá)數(shù)據(jù)457Geometric series等比數(shù)列436Gershgorin circles格爾什戈林圓491Gibbs phenomenon吉布斯效應(yīng)451Givens rotation吉文斯旋轉(zhuǎn)471Google谷歌368,

13、369,434Gram-Schmidt格拉姆-施密特223,234,236,241,370,469Graph圖表74,143,307,311,420,422,423Group群119,354HHalf-plane半平面7Heat equation熱方程式322,323Heisenberg海森堡305,310Hilbert space希爾伯特空間447,449Hookes Law虎克定律410,412Householder reflections鏡像變換237,469,472Hyperplane超平面30,42I Ill-conditioned matrix病態(tài)矩陣371,473,474Imag

14、inary虛數(shù)289Independent獨(dú)立的26,27,134,168,200,300Initial value初值313Inner product內(nèi)積11,56,108,448,502,506Input and output basis基底輸入輸出399Integral積分24,385,386Interior point method內(nèi)點(diǎn)法445Intersection of spaces交空間129,183Inverse matrix逆矩陣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約當(dāng)型356,357,358,361,482JPEG364,373KKalman filter卡爾曼濾波器93,214Kernel核377,380Kirchhoffs Laws基爾霍夫定律143,189,420,424-427Krylov克雷洛夫491,492Lnorm和范數(shù)225,480Lagrange multiplier拉格朗日乘子445Lanczos method蘭索斯方法490,492LAPACK線性代數(shù)軟件包98,237,486Leapfrog method跳步法317,329Least squar

16、es最小平方218,219,236,405,408,453Left nullspace左零空間184,186,192,425Left-inverse左逆的81,86,154,405Length長度12,232,447,448,501Line線34,40,221,474Line of springs線彈簧411Linear combination線性組合1,3Linear equation線性方程23Linear programming線性規(guī)劃440Linear transformation線性變換44,375-398Linearity線性關(guān)系44,245,246 Linearly indepe

17、ndent線性獨(dú)立26,134,168,169,200LINPACK線性系統(tǒng)軟件包465Loop環(huán)路307,425,426Lower triangular下三角9598,100,474Lucas numbers盧卡斯數(shù)306MMaple38,100Mathematica38,100MATLAB17,37,237,243,290,337,513Matrix(see full page 570)矩陣22,384,387Matrix exponential矩陣指數(shù)314,319,327Matrix multiplication矩陣乘法58,59,67,389Matrix notation矩陣記號37

18、Matrix space矩陣空間121,122,175,181,311Matrix矩陣-1,2,-1 matrix-1，2，-1矩陣106,167,261,265,349,374,410,480Adjacency, 鄰接矩陣74,80,311,369All-ones全1矩陣251,262,307,348Augmented增廣矩陣60,84,155Band帶狀矩陣99,468,469Block分塊矩陣70,94,115,266,348Circulant循環(huán)矩陣507,515Coefficient系數(shù)矩陣33,36Cofactor matrix伴隨矩陣270Companion友矩陣295,322C

19、omplex matrix復(fù)矩陣339,499Consumption消費(fèi)矩陣435,436Covariance協(xié)方差陣228,453,455,456,458Cyclic循環(huán)矩陣25,93,374Derivative導(dǎo)數(shù)矩陣385Difference差矩陣22,87,412Echelon梯矩陣137,143Eigenvalue matrix特征值矩陣298Eigenvector matrix特征向量矩陣298Elimination消元矩陣57,63,149Exponential指數(shù)矩陣314,319,327First difference一階差分矩陣22,373Fourier傅里葉矩陣394,4

20、93,505,510,511Hadamard阿達(dá)馬矩陣238,280Hermitian埃爾米特矩陣339,340,501,503,506,507Hessenberg黑森伯格矩陣262,488,492Hilbert希爾伯特矩陣92,254,348House宅矩陣378,382Hypercube超立方矩陣73Identity單位矩陣37,42,57,390Incidence關(guān)聯(lián)矩陣420,422,429Indefinite不定矩陣343Inverse逆矩陣24,81,270Invertible可逆矩陣27,83,86,112,408,574Jacobian雅可比矩陣274Jordan若爾當(dāng)矩陣35

21、6,358,462,565Laplacian( Graph Laplacian)（圖）拉普拉斯矩陣428Leslie萊斯利矩陣435,439Magic奇幻矩陣43Markov馬爾可夫矩陣43,285,294,369,373,431,437Negative definite負(fù)定矩陣343Nondiagonalizable不可對角化矩陣299,304,309Normal正規(guī)矩陣341,508,565Northwest西北矩陣119Nullspace matrix零空間矩陣136,147Orthogonal正交矩陣231,252,289Pascal帕斯卡矩陣66,72,88,101,348,359P

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

23、231,289,460,471Saddle-point鞍點(diǎn)矩陣115,343Second derivative (Hessian)二階導(dǎo)數(shù)（黑塞）矩陣349,353Second difference (1,-2,1)二階差分（1，-2，1）矩陣322,373,417Semidefinite半定矩陣345,415Shearing剪切矩陣379Similar相似矩陣355-362,400Sine matrix正弦矩陣349,354,373Singular奇異矩陣27,416,574Skew-symmetric反稱矩陣289,320,327,338,341Sparse稀疏矩陣100,470,474,

24、465Stable, 穩(wěn)定矩陣318Stiffness剛性矩陣317,409,412,419Stoichiometric化學(xué)計(jì)量矩陣430Sudoku數(shù)獨(dú)矩陣44Sum matrix和矩陣24,87,271Symmetric對稱矩陣109,330-341Translation平移矩陣459,463Triangular三角形矩陣95,236,247,271,289,335Tridiagonal三對角矩陣85,100,265,413,468,491Unitary酉矩陣504,505,506,510Vandermonde范德蒙德矩陣226,253,266,511Wavelet小波矩陣242Mean均

25、值228,453-457Minimum極小值349Multigrid多重網(wǎng)格485Multiplication by columns按列相乘23,36Multiplication by rows按行相乘36Multiplication count相乘次數(shù)68,80,99,467,469Multiplicity重?cái)?shù)304,358Multiplier乘子45,46,50,96Nchoose選442,454-dimensional space維空間1,120netlib100Network網(wǎng)絡(luò)420,427Newtons method牛頓法445No solution無解26,39,46,192No

26、ndiagonalizable不可對角化304,309Norm范數(shù)12,475,476,479,480,489Normal distribution正態(tài)分布455Normal equation正規(guī)方程210,211,453Normal matrix正規(guī)矩陣341,508,565Nullspace零空間132,185OOdd permutation奇置換113Ohms Law歐姆定律426Orthogonality正交性14,195,448Orthogonal complement正交補(bǔ)197,198,200Orthogonal spaces正交空間197Orthogonal subspaces

27、正交子空間195,196,204Orthogonal vectors正交向量14,195Orthonormal規(guī)范正交的230,234,240,504Orthonormal basis規(guī)范正交基367,368,449Orthonormal eigenvectors規(guī)范正交特征向量203,307,330,332,339,341,503PParabola拋物線224Parallelogram平行四邊形3,8,272,383Partial pivoting部分主元消元（法）113,466,467Particular solution特解155,156,159Permutation置換44,47,23

28、1,257Perpendicular(see Orthogonality)垂直12,14Perpendicular eigenvectors垂直特征向量203,339Perron-Frobenius Theorem佩龍-弗羅貝尼烏斯定理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主變元135,155Pixel,像素364,462Plane平面6,26Plane rotation,平面旋轉(zhuǎn)471Poisson

29、 distribution,泊松分布454Polar coordinates極坐標(biāo)274,281,495-497Polar decomposition極分解402,403Positive eigenvalues正特征值342Positive pivots正主元343Potential位勢423Power method（乘）冪法487Preconditioner預(yù)調(diào)節(jié)器481,486Principal axes主軸330Principal Component Analysis主成分分析457Probability概率432,453,454Product of pivots主元的積63,85,24

30、4,333Projection投影206-217,219,233Projection on line線上投影207,208Projection on subspace子空間上投影209,210Projective space射影空間460Pseudoniverse偽逆199,399,403,404,407Pythagoras畢達(dá)哥拉斯14,20PYTHON16,100Qfactorization分解243,564method方法360,487,490RRandom隨機(jī)21,55,348,373,562Range值域，區(qū)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實(shí)特征值330,331Recursion遞歸，遞推213,228,260,392,513Reduced cost縮減費(fèi)用443,444Reduced echelon form(rref)縮減梯形式85,134,138,148, 166,564Reflection鏡射（反射）232,243,286,336,471Regression回歸453Repeated eigenvalues重特征值299,320,322Residual剩余

32、（的）；殘差222,481,492Reverse order逆序82,107Right angle(see Orthogonality)直角14Right hand rule右手定則276Right-inverse右逆81,86,154,405Rotation旋轉(zhuǎn)2321,289,460,471,474Roundoff error舍入誤差371,466,477,478Row exchange行交換47,59,113,245,253Row picture行圖31,34,40Row reduced echelon form行縮減梯形式85Row space 行空間171,184SSaddle鞍點(diǎn)3

33、53Scalar標(biāo)量2,32Schur complementSchur補(bǔ)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二階差分316,322,336Second order equation二階方程314-317Shake a Stick474Shift移位375Sigma notation56Simplex method單純形法440,443Singular value奇異值363,365,371,476Singular Value Decomposition, see SVD奇異值分解Singular vector奇異向量363,408Skew-symmetric反對稱289,320,327,338,3