책 이미지
책 정보
· 분류 : 국내도서 > 대학교재/전문서적 > 자연과학계열 > 수학
· ISBN : 9791160731019
· 쪽수 : 568쪽
· 출판일 : 2018-03-20
목차
Chapter 1 Preliminaries
1.1 Fields _2
1.2 Matrices and Matrix Operations _8
Chapter 2 Vector Spaces
2.1 Vector Spaces _24
2.2 Vectors in Euclidean Spaces _33
2.3 Subspaces _45
2.4 Bases of Vector Spaces _54
Chapter 3 System of Linear Equations
3.1 Gauss-Jordan Elimination Method _78
3.2 Inverse Matrix _110
3.3 Elementary Matrix Multiplications _123
3.4 Row and Column Spaces _134
Chapter 4 Linear Transformations and Matrices
4.1 Linear Transformations _152
4.2 Matrix Representations of Linear Transformations _171
4.3 Compositions of Linear Transformations and Their Matrices _184
4.4 Change of Basis _191
Chapter 5 Determinants
5.1 Definition of Determinant _204
5.2 Properties of Determinant _215
5.3 Cramer’s Rule _227
Chapter 6 Inner Products
6.1 Inner Products _236
6.2 Gram-Schmidt Theorem _249
6.3 QR-Decomposition _271
Chapter 7 Eigenvalues and Their Applications
7.1 Cayley-Hamilton Theorem _278
7.2 Eigenvalues and Their Applications _290
7.3 Diagonalization of Square matrices _305
7.4 Diagonalization of Symmetric Matrices _321
7.5 Quadratic Forms _332
Chapter 8 Jordan Canonical Forms
8.1 Jordan Chains _352
8.2 Jordan Canonical Forms _369
Answers to Exercises _419
References _559
Index _561



















