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1、精选优质文档-倾情为你奉上高等代数Higher Algebra高等代数中的英文单词和短语第一章 多项式Chapter 1 Polynomials实系数多项式real coefficient polynomial有理系数多项式rational coefficient polynomial复系数多项式complex coefficient polynomial函数function多项式函数polynomial function带余除法division with remainder综合除法synthetic division公因式common factor最大公因式greatest common f
2、actor单因式unit-factor重因式repeated factor单根single root重根multiple root第二章 行列式Chapter 2 Determinants排列permutation对换transposition行列式determinant余子式cofactors term克拉默法则Cramer rule拉普拉斯定理Laplace theorem第三章 线性方程组Chapter 3 Systems of Linear Equations向量组vector system向量vector系数矩阵coefficient matrix线性方程组system of lin
3、ear equations线性组合linear combination线性相关linear dependence线性无关linear independence极大线性无关greatest linear independence线性表示linear expression基（基底）basis向量空间vector space秩rank齐次线性方程组system of homogeneous linear equations等价equivalent解solution矩阵相等equatity of matrices等价线性方程组equivalent linear system线性方程组的系数矩阵coef
4、ficient matrix of a linear system线性方程组的阶梯形echelon form of a linear system线性方程组的增广矩阵augmented matrix of a linear system高斯消元法gauss elimination method初等行运算elementary row operation行阶梯形矩阵row echelon matrix非平凡解nontrivial solution简化行阶梯形矩阵reduced row echelon matirx第四章 矩阵Chapter 4 Matrices单位矩阵identity matrix
5、方阵square matrix对角矩阵diagonal matrix初等矩阵elementary matrix伴随矩阵adjoint matrix满秩矩阵full-rank matrix零矩阵zero matrix行row行矩阵row matrix列column列矩阵column matrix上三角矩阵upper triangular matrix下三角矩阵lower triangular matrix矩阵的逆inverse of matrix矩阵的加法addition of matrix负矩阵negative matrix矩阵的乘法multiplication of matrix矩阵的标量乘
6、法scalar multiplication of matrix矩阵的转置transpose of matrix矩阵的列秩column rank of matrix矩阵的行秩row rank of matrix左分配率left distributive law右分配率right distributive law结合律associative law第五章 二次型Chapter 5 Quadratic Forms二次型quadratic form对称矩阵symmetric matrix线性替换linear substitution标准型normal form正定二次型positive defini
7、te quadratic form正定矩阵positive definite matrix非奇异线性变换nonsingular linear transformation第六章 线性空间Chapter 6 Linear Spaces线性空间linear space子空间subspace子空间的基basis of subspace子空间的生成元generators of subspace子空间的维数dimension of subspace同构空间isomorphism space一一映射one-to-one mapping线性映射的逆inverse of linear mapping同构iso
8、morphism零映射（函数）zero mapping (function)域field最大线性无关组maximal set of linear independence满射surjection第七章 线性变换Chapter 7 Linear Transformations线性变换linear transformation特征值eigenvalue特征向量eigenvector特征多项式characteristic polynomial哈密顿-凯莱定理Hamilton-Cayley theorem方阵的特征值eigenvalue of square matrix方阵的特征向量eigenvect
9、or of square matrix矩阵的迹trace of matrix核kernel矩阵的特征多项式characteristic polynomial of matrix特征值的重数multiplicity of eigenvalue迹trace相似矩阵similar matrix可对角化矩阵diagonalizable matrix第八章 -矩阵Chapter 8 -Matrices若尔当典范形Jordan canonical form行列式因子determinant factor不变因子invariant factor初等因子elementary factor初等变换elementa
10、ry transformation第九章 欧几里得空间Chapter 9 Euclidean Space度量矩阵metric matrix正交基orthogonal basis标准正交基normal orthogonal basis正交矩阵orthogonal matrix正交向量orthogonal vector实对称矩阵real symmetric matrix内积dot product向量的长度length of vector施密特正交化矩阵Schmidt orthogonalization process第十章 双线性函数Chapter 10 Bilinear Fucntions双线性函数bilinear function对偶基dual basis对偶空间dual space反对称双线性函数antisymmetric bilinear function对称双线性函数symmetric bilinear function专心-专注-专业