高等代数英语词汇

bysahuHigherAlgebra第一章多项式chapter1Polynomialsrealcoefficientpolynomial实多项式系数commonfactor公因式rationalcoefficientpolynomial有理数多项式系数greatestcommonfactor昀大公因式complexcoefficientpolynomial复系数多项式unit-factor单因式function函数repeatedfactor重因式polynomialfunction多项式函数singleroot单根divisionwithremainder带余除法multipleroot重根syntheticdivision综合除法第二章行列式Chapter2Determinantspermutation排列cofactorsterm余子式transposition对换Cramerrule克拉默法则determinant行列式Laplacetheorem拉普拉斯定理第三章线性方程组Chapter3SystemsofLinearEquationscoefficientmatrix系数矩阵linearexpression线性表示systemoflinearequations线性方程组basis基（基底）linearcombination线性组合vectorspace向量空间lineardependence线性相关rank秩linearindependence线性无关equivalent等价greatestlinearindependence极大线性无关solution解equivalentlinearsystem等价线性方程组equalityofmatrices矩阵相等gausseliminationmethod高斯消元法vectorsystem向量组elementaryrowoperation初等行运算vector向量rowechelonmatrix行阶梯形矩阵nontrivialsolution非平凡解reducedrowechelonmatrix简化行阶梯形矩阵systemofhomogeneouslinearequations齐次线性方程组coefficientmatrixofalinearsystem线性方程组的系数矩阵echelonformofalinearsystem线性方程组的阶梯形augmentedmatrixofalinearsystem线性方程组的增广矩阵bysahu第四章矩阵Chapter4Matricesidentitymatrix单位矩阵squarematrix方阵diagonalmatrix对角矩阵elementarymatrix初等矩阵adjointmatrix伴随矩阵full-rankmatrix满秩矩阵zeromatrix零矩阵row行rowmatrix行矩阵column列columnmatrix列矩阵uppertriangularmatrix上三角矩阵lowertriangularmatrix下三角矩阵inverseofmatrix矩阵的逆additionofmatrix矩阵的加法negativematrix负矩阵multiplicationofmatrix矩阵的乘法transposeofmatrix矩阵的转置scalarmultiplicationofmatrix矩阵的标量乘法columnrankofmatrix矩阵的列秩rowrankofmatrix矩阵的行秩leftdistributivelaw左分配律rightdistributivelaw右分配律associativelaw结合律第五章二次型Chapter5QuadraticFormsquadratic二次型symmetricmatrix对称矩阵linearsubstitution线性替换normalform标准型positivedefinitequadraticform正定二次型positivedefinitematrix正定矩阵nonsingularlineartransformation非奇异线性变换第六章线性空间Chapter6LinearSpaceslinearspace线性空间subspace子空间basisofsubspace子空间的基surjection满射dimensionofsubspace子空间的维数isomorphism同构one-to-onemapping一一映射isomorphismspace同构空间zeromapping(function)零映射（函数）field域generatorsofsubspace子空间生成的元maximalsetoflinearindependence昀大线性无关组第七章线性变换Chapter7LinearTransformationslineartransformation线性变换eigenvalue特征值eigenvector特征向量kernel核characteristicpolynomial特征多项式trace迹Hamilton-Cayleytheorem哈密顿-凯莱定理traceofmatrix矩阵的迹eigenvalueofsquarematrix方阵的特征值similarmatrix相似矩阵eigenvectorofsquarematrix方阵的特征向量diagonalizablematrix可对角化矩阵multiplicityofeigenvalue特征值的重数characteristicpolynomialofmatrix矩阵的特征多项式bysahu第八章λ矩阵Chapter8λ-MatricesJordancanonicalform若尔当标准型determinantfactor行列式因子invariantfactor不变因子elementaryfactor初等因子elementarytransformation初等变换第九章欧几里得空间Chapter9EuclideanSpacemetricmatrix度量矩阵orthogonalbasis正交基normalorthogonalbasis标准正交基orthogonalmatrix正交矩阵orthogonalvector正交向量dotproduct内积realsymmetricmatrix实对称矩阵lengthofvector向量长度Schmidtorthogonalizationprocess施密特正交化矩阵第十章双线性函数Chapter10BilinearFunctionbilinearfunction双线性函数dualbasis对偶基antisymmetricbilinearfunction反对称双线性函数dualspace对偶空间symmetricbilinearfunction对称双线性函数