線性代數(shù)課程專業(yè)詞匯表

線性代數(shù)課程專業(yè)詞匯表英文單詞或詞組中文翻譯書中出現(xiàn)頁碼Linearequation線性方程1Linearsystem(s)線性方程組1Consistent有解2Inconsistent無解2Solutionsetoflinearsystem線性方程組的解會合2Equivalentsystems等價的線性方程組3Rowoperations行變換5Stricttriangularform嚴格三角形式5Backsubstitution回代法6Equivalentsystems等價的線性方程組6Coefficientmatrix系數(shù)矩陣7Coefficientmatrix系數(shù)矩陣7Augmentedmatrix增廣矩陣8Pivot主元8Freevariables自由未知量14Leadvariables前變量14Gaussianelimination高斯消元法15Overdeterminedlinearsystem方程個數(shù)超出未知數(shù)個數(shù)的方程組15Rowechelonform行階梯形15Underdeterminedlinearsystem方程個數(shù)低于未知數(shù)個數(shù)的方程組17Gauss-Jordanreduction高斯-若當概括法18Reducedrowechelonform減少的行階梯形18Homogeneouslinearsystem齊次線性方程組22Homogeneoussystem齊次線性方程組22nontrivialsolution非零解22Trivialsolution平庸解，全零解22Matrixalgebra矩陣代數(shù)30Scalars常數(shù)30Columnvector(s)列向量31Euclideann-space歐幾里得空間31Rowvector(s)行向量31Vector(s）向量31Additionofmatrices矩陣加法32Additionofmatrices矩陣加法32Equalityofmatrices矩陣相等32Scalarmultiplicationformatrices矩陣的數(shù)乘32Scalarmultiplicationofmatrices矩陣的數(shù)乘32Zeromatrix?零矩陣33Scalarproduct內積34Linearcombination線性組合36ConsistencyTheorem解的存在性定理37Multiplicationofmatrices矩陣乘法38Identitymatrix單位矩陣47Inversematrix逆矩陣48Invertiblematrix可逆矩陣48Nonsingularmatrix非奇怪矩陣48Singularmatrix奇怪矩陣49Transposeofamatrix矩陣的轉置49Transposeofmatrix矩陣的轉置49Symmetricmatrix對稱矩陣51Symmetricmatrix對稱矩陣51Adjacencymatrix毗鄰矩陣52Graph(s)圖52Anglebetweenvectors向量的夾角56Markovchain(s）Markov鏈57Elementarymatrix初等矩陣62Rowequivalent行等價64Rowequivalentmatrices行等價矩陣64Diagonalmatrix對角矩陣67Lowertriangular下三角67Triangularfactorization三角分解67Triangularmatrix三角形矩陣67Triangularmatrix三角形矩陣67Uppertriangular上三角67Uppertriangularmatrix上三角矩陣67LUfactorizationLU分解68Matrixfactorizations矩陣分解68Partitionedmatrices分塊矩陣72Vandermondematrix范德蒙矩陣72Blockmultiplication分塊乘法74Innerproduct內積78Determinant(s)隊列式90Cofactor代數(shù)余子式93Minor余子式93Cofactorexpansion代數(shù)余子式睜開94Determinantofmatrix矩陣的隊列式95Skewsymmetric反對稱105Adjointofamatrix陪伴矩陣106Cramer’srule克萊姆法例107Cryptography密碼學108Additionofvectors向量的加法119Closureproperties關閉性119Vectorspace向量空間119Zerovector零向量119C[a,b]區(qū)間[a,b]上的連續(xù)函數(shù)120Isomorphismbetweenvectorspaces向量空間的同構123Subspace(s)子空間123Zerosubsapce零空間125Nullspace零化空間127Nullspaceofmatrix矩陣的零化空間127Span張成128Spanningset生成集129Linearlydependent線性有關136Linearlyindependent線性沒關136Basis基145Dimension?維數(shù)147Finitedimensional有限維147Infinitedimensional無窮維147Standardbasis標準基150changeofbasis基的變換151Coordinatevector坐標向量152Transitionmatrix過渡矩陣155Coordinates坐標157Columnspace?列空間162Columnspaceofmatrix矩陣的列空間162Rankofamatrix矩陣的秩162Rankofmatrix矩陣的秩162Rowspace行空間162Rowspaceofmatrix矩陣的行空間162Nullity零化度164Rank-NullityTheoremRank-Nullity定理164Leftinverse左可逆170Rightinverse右逆170Fullrank滿秩171Lineartransformation(s)線性變換175Linearoperator線性算子176Image象181Kernel核181Contraction縮短192Dilation擴充192Similarity相像性199Similarmatrices相像矩陣202Trace跡206Anglebetweenvectors向量的夾角211Euclideanlength歐幾里得長度211Distancein2-space2維空間的距離212Cauchy-Schwarzinequality柯西-施瓦茲不等式213Orthogonality正交性213Scalarprojection數(shù)目投影214equationofplane平面方程215Nonmalvector正規(guī)向量215Anglebetweenvectors向量的夾角216PythagoreanLawPythagorean定理216Correlations有關?219Correlationmatrix有關矩陣221Covariance協(xié)方差222Covariancematrix協(xié)方差矩陣222Factoranalysis因子剖析222Fundamentalsubspaces基簿本空間227Rangeofamatrix矩陣的值域227Directsum直和229Leastsquaresproblem(s)最小二乘法問題234Projectionontocolumnspace列空間上的投射236Normalequations正規(guī)方程237Innerproductspace內積空間245Lengthininnerproductspaces內積空間中的長度246Orthogonalset(s)正交會合255Orthonormalset(s)標準正交集255orthonormalbasis標準正交基256Orthonormalbasis標準正交基256Orthogonalmatrices正交矩陣258Orthogonalmatrix正交矩陣258Approximationoffunctions函數(shù)的迫近264Fouriercoefficients傅里葉系數(shù)266Fouriermatrix傅里葉矩陣269Gram-SchmidtprocessGram-Schmidt過程274DimensionTheorem維數(shù)定理283Orthogonalpolynomials正交多項式283HermitepolynomialsHermite多項式287JacobipolynomialsJacobi多項式287Lagrange’sinterpolatingformulaLagrange插值公式288Gaussianquadrature高斯求積289Characteristicvalue(s)特點值301Characteristicvector特點向量301Eigenvalue特點值301Eigenvector特點向量301Characteristicequation特點方程302Characteristicpolynomial特點多項式302Eigenspace特點空間302Nilpotent冪零的311Companionmatrix友矩陣313Lineardifferentialequations線性微分方程313Initialvalueproblems?初值問題314Diagonalizablematrix可對角化的矩陣326Distanceinn-spacen維空間的距離332Complexmatrix復矩陣346HermitematrixHermite矩陣346Unitarymatrix酉矩陣347Unitarymatrix酉矩陣347Normalmatrices正規(guī)矩陣351Singularvalues奇怪值356Conicsections二次曲線部分371Quadraticequationinnvariablesn個變量的二次方程376Quadraticforminnvariablesn個變量的二次型376Definitequadraticform定二次型378Indefinitequadraticform不定二次型378Negativedefinitematrix負定矩陣378Negativedefinitequadraticform負定二次型378Negativesemidefinitematrix半負定矩陣378Negativesemidefinitequadraticform半負定二次型378Positivedefinitematrix正定矩陣378Positivedefinitequadraticform正定二次型378Positivesemidefinitematrix半正定矩陣378Positivesemidefinitequadraticform半正定二次型378Localmaximum極大值382Localminimum極小值382Positivedefinitematrix正定矩陣384Leadingprinci