高等代數中的英文單詞和短語

1、精選優(yōu)質文檔-傾情為你奉上高等代數Higher Algebra高等代數中的英文單詞和短語第一章 多項式Chapter 1 Polynomials實系數多項式real coefficient polynomial有理系數多項式rational coefficient polynomial復系數多項式complex coefficient polynomial函數function多項式函數polynomial function帶余除法division with remainder綜合除法synthetic division公因式common factor最大公因式greatest common f

2、actor單因式unit-factor重因式repeated factor單根single root重根multiple root第二章 行列式Chapter 2 Determinants排列permutation對換transposition行列式determinant余子式cofactors term克拉默法則Cramer rule拉普拉斯定理Laplace theorem第三章 線性方程組Chapter 3 Systems of Linear Equations向量組vector system向量vector系數矩陣coefficient matrix線性方程組system of lin

3、ear equations線性組合linear combination線性相關linear dependence線性無關linear independence極大線性無關greatest linear independence線性表示linear expression基（基底）basis向量空間vector space秩rank齊次線性方程組system of homogeneous linear equations等價equivalent解solution矩陣相等equatity of matrices等價線性方程組equivalent linear system線性方程組的系數矩陣coef

4、ficient matrix of a linear system線性方程組的階梯形echelon form of a linear system線性方程組的增廣矩陣augmented matrix of a linear system高斯消元法gauss elimination method初等行運算elementary row operation行階梯形矩陣row echelon matrix非平凡解nontrivial solution簡化行階梯形矩陣reduced row echelon matirx第四章 矩陣Chapter 4 Matrices單位矩陣identity matrix

5、方陣square matrix對角矩陣diagonal matrix初等矩陣elementary matrix伴隨矩陣adjoint matrix滿秩矩陣full-rank matrix零矩陣zero matrix行row行矩陣row matrix列column列矩陣column matrix上三角矩陣upper triangular matrix下三角矩陣lower triangular matrix矩陣的逆inverse of matrix矩陣的加法addition of matrix負矩陣negative matrix矩陣的乘法multiplication of matrix矩陣的標量乘

6、法scalar multiplication of matrix矩陣的轉置transpose of matrix矩陣的列秩column rank of matrix矩陣的行秩row rank of matrix左分配率left distributive law右分配率right distributive law結合律associative law第五章 二次型Chapter 5 Quadratic Forms二次型quadratic form對稱矩陣symmetric matrix線性替換linear substitution標準型normal form正定二次型positive defini

7、te quadratic form正定矩陣positive definite matrix非奇異線性變換nonsingular linear transformation第六章 線性空間Chapter 6 Linear Spaces線性空間linear space子空間subspace子空間的基basis of subspace子空間的生成元generators of subspace子空間的維數dimension of subspace同構空間isomorphism space一一映射one-to-one mapping線性映射的逆inverse of linear mapping同構iso

8、morphism零映射（函數）zero mapping (function)域field最大線性無關組maximal set of linear independence滿射surjection第七章 線性變換Chapter 7 Linear Transformations線性變換linear transformation特征值eigenvalue特征向量eigenvector特征多項式characteristic polynomial哈密頓-凱萊定理Hamilton-Cayley theorem方陣的特征值eigenvalue of square matrix方陣的特征向量eigenvect

9、or of square matrix矩陣的跡trace of matrix核kernel矩陣的特征多項式characteristic polynomial of matrix特征值的重數multiplicity of eigenvalue跡trace相似矩陣similar matrix可對角化矩陣diagonalizable matrix第八章 -矩陣Chapter 8 -Matrices若爾當典范形Jordan canonical form行列式因子determinant factor不變因子invariant factor初等因子elementary factor初等變換elementary transformation第九章 歐幾里得空間Chapter 9 Euclidean Space度量矩陣metric matrix正交基orthogonal basis標準正交基normal orthogonal basis正交矩陣orthogonal matrix正交向量orthogonal vector實對稱矩陣real symmetric matrix內積dot product向量的長度length of vector施密特正交化矩陣Schmidt orthogonalization process第十章 雙線性函數Cha