线性代数课程专业词汇表

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1Linearsystem(s)线性方程组1Consistent有解2Inconsistent无解2Solutionsetoflinearsystem线性方程组的解集合2Equivalentsystems等价的线性方程组3Rowoperations行变换5Stricttriangularform严格三角形式5Backsubstitution回代法6Equivalentsystems等价的线性方程组6Coefficientmatrix系数矩阵7Coefficientmatrix系数矩阵7Augmentedmatrix增广矩阵8Pivot主元8Freevariables自由未知量14Leadvariables前变量14Gaussianelimination高斯消元法15Overdeterminedlinearsystem方程个数超过未知数个数的方程组15Rowechelonform行阶梯形15Underdeterminedlinearsystem方程个数低于未知数个数的方程组17Gauss-Jordanreduction高斯-若当归纳法18Reducedrowechelonform减少的行阶梯形18Homogeneouslinearsystem齐次线性方程组22Homogeneoussystem齐次线性方程组22nontrivialsolution非零解22Trivialsolution平凡解，全零解22Matrixalgebra矩阵代数30Scalars常数30Columnvector(s)列向量31Euclideann-space欧几里得空间31Rowvector(s)行向量31Vector(s）向量31Additionofmatrices矩阵加法32Additionofmatrices矩阵加法32Equalityofmatrices矩阵相等32Scalarmultiplicationformatrices矩阵的数乘32Scalarmultiplicationofmatrices矩阵的数乘32Zeromatrix零矩阵33Scalarproduct内积34Linearcombination线性组合36ConsistencyTheorem解的存在性定理37Multiplicationofmatrices矩阵乘法38Identitymatrix单位矩阵47Inversematrix逆矩阵48Invertiblematrix可逆矩阵48Nonsingularmatrix非奇异矩阵48Singularmatrix奇异矩阵49Transposeofamatrix矩阵的转置49Transposeofmatrix矩阵的转置49Symmetricmatrix对称矩阵51Symmetricmatrix对称矩阵51Adjacencymatrix邻接矩阵52Graph(s)图52Anglebetweenvectors向量的夹角56Markovchain(s）Markov链57Elementarymatrix初等矩阵62Rowequivalent行等价64Rowequivalentmatrices行等价矩阵64Diagonalmatrix对角矩阵67Lowertriangular下三角67Triangularfactorization三角分解67Triangularmatrix三角形矩阵67Triangularmatrix三角形矩阵67Uppertriangular上三角67Uppertriangularmatrix上三角矩阵67LUfactorizationLU分解68Matrixfactorizations矩阵分解68Partitionedmatrices分块矩阵72Vandermondematrix范德蒙矩阵72Blockmultiplication分块乘法74Innerproduct内积78Determinant(s)行列式90Cofactor代数余子式93Minor余子式93Cofactorexpansion代数余子式展开94Determinantofmatrix矩阵的行列式95Skewsymmetric反对称105Adjointofamatrix伴随矩阵106Cramer’srule克莱姆法则107Cryptography密码学108Additionofvectors向量的加法119Closureproperties封闭性119Vectorspace向量空间119Zerovector零向量119C[a,b]区间[a,b]上的连续函数120Isomorphismbetweenvectorspaces向量空间的同构123Subspace(s)子空间123Zerosubsapce零空间125Nullspace零化空间127Nullspaceofmatrix矩阵的零化空间127Span张成128Spanningset生成集129Linearlydependent线性相关136Linearlyindependent线性无关136Basis基145Dimension维数147Finitedimensional有限维147Infinitedimensional无限维147Standardbasis标准基150changeofbasis基的变换151Coordinatevector坐标向量152Transitionmatrix过渡矩阵155Coordinates坐标157Columnspace列空间162Columnspaceofmatrix矩阵的列空间162Rankofamatrix矩阵的秩162Rankofmatrix矩阵的秩162Rowspace行空间162Rowspaceofmatrix矩阵的行空间162Nullity零化度164Rank-NullityTheoremRank-Nullity定理164Leftinverse左可逆170Rightinverse右逆170Fullrank满秩171Lineartransformation(s)线性变换175Linearoperator线性算子176Image象181Kernel核181Contraction收缩192Dilation扩张192Similarity相似性199Similarmatrices相似矩阵202Trace迹206Anglebetweenvectors向量的夹角211Euclideanlength欧几里得长度211Distancein2-space2维空间的距离212Cauchy-Schwarzinequality柯西-施瓦兹不等式213Orthogonality正交性213Scalarprojection数量投影214equationofplane平面方程215Nonmalvector正规向量215Anglebetweenvectors向量的夹角216PythagoreanLawPythagorean定理216Correlations相关219Correlationmatrix相关矩阵221Covariance协方差222Covariancematrix协方差矩阵222Factoranalysis因子分析222Fundamentalsubspaces基本子空间227Rangeofamatrix矩阵的值域227Directsum直和229Leastsquaresproblem(s)最小二乘法问题234Projectionontocolumnspace列空间上的投射236Normalequations正规方程237Innerproductspace内积空间245Lengthininnerproductspaces内积空间中的长度246Orthogonalset(s)正交集合255Orthonormalset(s)标准正交集255orthonormalbasis标准正交基256Orthonormalbasis标准正交基256Orthogonalmatrices正交矩阵258Orthogonalmatrix正交矩阵258Approximationoffunctions函数的逼近264Fouriercoefficients傅里叶系数266Fouriermatrix傅里叶矩阵269Gram-SchmidtprocessGram-Schmidt过程274DimensionTheorem维数定理283Orthogonalpolynomials正交多项式283HermitepolynomialsHermite多项式287JacobipolynomialsJacobi多项式287Lagrange’sinterpolatingformulaLagrange插值公式288Gaussianquadrature高斯求积289Characteristicvalue(s)特征值301Characteristicvector特征向量301Eigenvalue特征值301Eigenvector特征向量301Characteristicequation特征方程302Characteristicpolynomial特征多项式302Eigenspace特征空间302Nilpotent幂零的311Companionmatrix友矩阵313Lineardifferentialequations线性微分方程313Initialvalueproblems初值问题314Diagonalizablematrix可对角化的矩阵326Distanceinn-spacen维空间的距离332Complexmatrix复矩阵346HermitematrixHermite矩阵346Unitarymatrix酉矩阵347Unitarymatrix酉矩阵347Normalmatrices正规矩阵351Singularvalues奇异值356Conicsections二次曲线部分371Quadraticequationinnvariablesn个变量的二次方程376Quadraticforminnvariablesn个变量的二次型376Definitequadraticform定二次型378Indefinitequadraticform不定二次型378Negativedefinitematrix负定矩阵378Negativedefinitequadraticform负定二次型378Negativesemidefinitematrix半负定矩阵378Negativesemidefinitequadraticform半负定二次型378Positivedefinitematrix正定矩阵378Positivedefinitequadraticform正定二次型378Positivesemidefinitematrix半正定矩阵378Positivesemidefinitequadraticform半正定二次型378Localmaximum极大值382Localminimum极小值382Positivedefinitematrix正定矩阵384Leadingprincipalsubmatrix顺序主子矩阵385Nonnegativematrix非负矩阵392Nonnegativevector非负向量392Positivematrix正矩阵392Positivematrix正矩阵392Reduciblematrix可约矩阵394FrobeniustheoremFrobenius定理395Absoluteerror绝对误差411Relativeerror相对误差411Backsubstitution回代法419QRfactorizationQR分解448