线性代数课程专业词汇表.doc
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线性代数课程专业词汇表
英文单词或词组中文翻译书中出现页码
Linearequation线性方程1
Linearsystem(s)线性方程组1
Consistent有解2
Inconsistent无解2
Solutionsetoflinearsystem线性方程组的解集合2
Equivalentsystems等价的线性方程组3
Rowoperations行变换5
Stricttriangularform严格三角形式5
Backsubstitution回代法6
Equivalentsystems等价的线性方程组6
Coefficientmatrix系数矩阵7
Coefficientmatrix系数矩阵7
Augmentedmatrix增广矩阵8
Pivot主元8
Freevariables自由未知量14
Leadvariables前变量14
Gaussianelimination高斯消元法15
Overdeterminedlinearsystem方程个数超过未知数个数的方程组15
Rowechelonform行阶梯形15
Underdeterminedlinearsystem方程个数低于未知数个数的方程组17
Gauss-Jordanreduction高斯-若当归纳法18
Reducedrowechelonform减少的行阶梯形18
Homogeneouslinearsystem齐次线性方程组22
Homogeneoussystem齐次线性方程组22
nontrivialsolution非零解22
Trivialsolution平凡解,全零解22
Matrixalgebra矩阵代数30
Scalars常数30
Columnvector(s)列向量31
Euclideann-space欧几里得空间31
Rowvector(s)行向量31
Vector(s)向量31
Additionofmatrices矩阵加法32
Additionofmatrices矩阵加法32
Equalityofmatrices矩阵相等32
Scalarmultiplicationformatrices矩阵的数乘32
Scalarmultiplicationofmatrices矩阵的数乘32
Zeromatrix 零矩阵33
Scalarproduct内积34
Linearcombination线性组合36
ConsistencyTheorem解的存在性定理37
Multiplicationofmatrices矩阵乘法38
Identitymatrix单位矩阵47
Inversematrix逆矩阵48
Invertiblematrix可逆矩阵48
Nonsingularmatrix非奇异矩阵48
Singularmatrix奇异矩阵49
Transposeofamatrix矩阵的转置49
Transposeofmatrix矩阵的转置49
Symmetricmatrix对称矩阵51
Symmetricmatrix对称矩阵51
Adjacencymatrix邻接矩阵52
Graph(s)图52
Anglebetweenvectors向量的夹角56
Markovchain(s)Markov链57
Elementarymatrix初等矩阵62
Rowequivalent行等价64
Rowequivalentmatrices行等价矩阵64
Diagonalmatrix对角矩阵67
Lowertriangular下三角67
Triangularfactorization三角分解67
Triangularmatrix三角形矩阵67
Triangularmatrix三角形矩阵67
Uppertriangular上三角67
Uppertriangularmatrix上三角矩阵67
LUfactorizationLU分解68
Matrixfactorizations矩阵分解68
Partitionedmatrices分块矩阵72
Vandermondematrix范德蒙矩阵72
Blockmultiplication分块乘法74
Innerproduct内积78
Determinant(s)行列式90
Cofactor代数余子式93
Minor余子式93
Cofactorexpansion代数余子式展开94
Determinantofmatrix矩阵的行列式95
Skewsymmetric反对称105
Adjointofamatrix伴随矩阵106
Cramer’srule克莱姆法则107
Cryptography密码学108
Additionofvectors向量的加法119
Closureproperties封闭性119
Vectorspace向量空间119
Zerovector零向量119
C[a,b]区间[a,b]上的连续函数120
Isomorphismbetweenvectorspaces向量空间的同构123
Subspace(s)子空间123
Zerosubsapce零空间125
Nullspace零化空间127
Nullspaceofmatrix矩阵的零化空间127
Span张成128
Spanningset生成集129
Linearlydependent线性相关136
Linearlyindependent线性无关136
Basis基145
Dimension 维数147
Finitedimensional有限维147
Infinitedimensional无限维147
Standardbasis标准基150
changeofbasis基的变换151
Coordinatevector坐标向量152
Transitionmatrix过渡矩阵155
Coordinates坐标157
Columnspace 列空间162
Columnspaceofmatrix矩阵的列空间162
Rankofamatrix矩阵的秩162
Rankofmatrix矩阵的秩162
Rowspace行空间162
Rowspaceofmatrix矩阵的行空间162
Nullity零化度164
Rank-NullityTheoremRank-Nullity定理164
Leftinverse左可逆170
Rightinverse右逆170
Fullrank满秩171
Lineartransformation(s)线性变换175
Linearoperator线性算子176
Image象181
Kernel核181
Contraction收缩192
Dilation扩张192
Similarity相似性199
Similarmatrices相似矩阵202
Trace迹206
Anglebetweenvectors向量的夹角211
Euclideanlength欧几里得长度211
Distancein2-space2维空间的距离212
Cauchy-Schwarzinequality柯西-施瓦兹不等式213
Orthogonality正交性213
Scalarprojection数量投影214
equationofplane平面方程215
Nonmalvector正规向量215
Anglebetweenvectors向量的夹角216
PythagoreanLawPythagorean定理216
Correlations相关 219
Correlationmatrix相关矩阵221
Covariance协方差222
Covariancematrix协方差矩阵222
Factoranalysis因子分析222
Fundamentalsubspaces基本子空间227
Rangeofamatrix矩阵的值域227
Directsum直和229
Leastsquaresproblem(s)最小二乘法问题234
Projectionontocolumnspace列空间上的投射236
Normalequations正规方程237
Innerproductspace内积空间245
Lengthininnerproductspaces内积空间中的长度246
Orthogonalset(s)正交集合255
Orthonormalset(s)标准正交集255
orthonormalbasis标准正交基256
Orthonormalbasis标准正交基256
Orthogonalmatrices正交矩阵258
Orthogonalmatrix正交矩阵258
Approximationoffunctions函数的逼近264
Fouriercoefficients傅里叶系数266
Fouriermatrix傅里叶矩阵269
Gram-SchmidtprocessGram-Schmidt过程274
DimensionTheorem维数定理283
Orthogonalpolynomials正交多项式283
HermitepolynomialsHermite多项式287
JacobipolynomialsJacobi多项式287
Lagrange’sinterpolatingformulaLagrange插值公式288
Gaussianquadrature高斯求积289
Characteristicvalue(s)特征值301
Characteristicvector特征向量301
Eigenvalue特征值301
Eigenvector特征向量301
Characteristicequation特征方程302
Characteristicpolynomial特征多项式302
Eigenspace特征空间302
Nilpotent幂零的311
Companionmatrix友矩阵313
Lineardifferentialequations线性微分方程313
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