矩陣理論及其應用 (英文) 邱啟榮韓勵佳魏軍強 9787030757388 【台灣高等教育出版社】

Name: 矩陣理論及其應用 (英文) 邱啟榮 韓勵佳 魏軍強 9787030757388 【台灣高等教育出版社】
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原出版社：科學

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書名：矩陣理論及其應用 (英文)
ISBN：9787030757388
出版社：科學
著編譯者：邱啟榮韓勵佳魏軍強
頁數：197
所在地：中國大陸 *此為代購商品
書號：1601173
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內容簡介

本書是一本適合工科的留學研究生使用的教材，此外又適合國內研究生作為英文輔助教材使用。本書內容全面，系統性強，涵蓋了國內工科研究生對矩陣論的幾乎全部知識點，並在教學結構上進行了創新的優化和調整。本書包含六章內容。其中第一章為對線性代數知識的回顧，第二章介紹線性空間的定義、賦范線性空間、內積空間；第三章介紹線性變換；第四章介紹若當標準型及詳細的矩陣分析及矩陣函數等內容；第五章介紹矩陣分解、廣義逆、Kronecor積等及其在求解矛盾方程組和矩陣方程中的各種應用。本書更好的體現了知識的融會貫通及應用。

Chapter 1 Basics of Linear Algebra
1 1 Basic operations of matrices
1 1 1 Addition for matrices
1 1 2 Scalar multiplication of matrix A
1 1 3 Matrix multiplication
1 1 4 Identity matrix
1 1 5 Transposition matrix and conjugate transpose of matrix A
1 1 6 Matrix inversion
1 1 7 Symmetries
1 2 Determinants
1 2 1 Determinant definition
1 2 2 Properties of determinants
1 2 3 Cofactor
1 2 4 Cramer's rule
1 3 Elementary operations
1 3 1 Elementary row transformation
1 3 2 Reduced echelon form
1 3 3 Rank of matrix
1 3 4 Solving equations by elementary transformation
1 4 Linear independence
1 5 Exercises
Chapter 2 Linear Space
2 1 Set and map
2 2 Linear space
2 3 Basis， dimension and coordinates
2 4 Change of basis
2 5 Exercises
Chapter 3 Normed Linear Space and Inner Product Space
3 1 Normed linear space and matrix norm
3 1 1 Normed linear space
3 1 2 Norm of matrix
3 2 Inner product spaces
3 2 1 Inner product
3 2 2 Representation of inner product
3 2 3 Orthogonality and Schmidt's orthogonalization method
3 3 Application of norm-preliminary matrix analysis
3 3 1 The limit of matrix sequence
3 3 2 Matrix series
3 3 3 Matrix power series
3 3 4 Differentiation and integration of matrices
3 4 Exercises
Chapter 4 Linear Transformation
4 1 Linear transformation
4 2 Matrix of linear transformation
4 3 Eigenvalues and eigenvectors
4 4 Eigenvalues and eigenvectors for matrix
4 5 Exercises
Chapter 5 Jordan Normal Form of Matrix and Matrix Function
5 1 Diagonalization
5 2 Jordan normal form of matrix A
5 3 Minimum polynomial
5 4 Matrix functions
5 4 1 Matrix function by infinite series
5 4 2 General definition and calculation of matrix function
5 4 3 Applications
5 5 Exercises
Chapter 6 Applications of Matrix Theory in Linear Equations and Matrix Equations
6 1 Matrix factorization and application in linear equations
6 1 1 The LU factorization and applications
6 1 2 Applications in solving linear equations
6 2 Minus inverse and applications in compatible linear equations
6 3 Plus inverse of matrix and the minimal norm least square solutions of linear equations
6 3 1 Full rank factorization of matrix
6 3 2 Plus inverse of matrix
6 3 3 Minimal norm least square solution of linear equations
6 4 Kronecker product and applications in matrix equations
6 4 1 Definitions and properties of Kronecker product
6 4 2 Applications in matrix equations
6 5 Exercises
References

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