Table of Contents
Chapter 1 Vector Space 1 1 Definition .
2
2 bases.
10
3 Dimension of vector space.
15
4. Sum and direct.
19

Chapter 2 Matrix 23 1 Matrix space.
23
2nd linear equation.
29
3. Multiplication of matrices.
32

Chapter 3 Linear Mapping 45 1 Mapping.
45
2 linear mapping.
53
3 The core and phase of linear thinking.
61
4 Synthesis and history of linear thought.
68
5 Geometric Applications.
75

Chapter 4 Linear Mapping and Matrices 85 1 Linear mappings corresponding to matrices.
85
2. Matrix corresponding to linear mapping.
86
3 Bases, matrices, linear mappings.
92

Chapter 5 Scalar Inner Product and Orthogonality 101 1 Scalar Inner Product .
101
2. For orthogonal bases and positive definite signs.
109
Application to linear equations, coefficients.
119

Chapter 6 Determinant 147 1 Second order determinant .
147
2 Existence of determinants.
150
3 Other properties of determinants.
158
4 Kramer's Law.
165
Triangulation of matrices by 5-column operations.
169
6 Substitution .
171
7 Expansion and uniqueness of determinants.
176
8 Inverse matrix.
182
9 Coefficients and subdeterminants of matrices.
186

Chapter 7: Symmetry Operators, Hermitian Operators, and Unitary Operators 189
1 Symmetry operator.
189
2 Hermitian operators.
193
3 Unitary working units.
198

Chapter 8 Eigenvectors and Eigenvalues ​​203
1 Eigenvectors and eigenvalues.
203
2 characteristic polynomials.
209
3 Eigenvalues ​​and eigenvectors of a symmetric matrix.
223
4 Diagonalization of symmetric linear maps.
228
5 For Hermit.
234
6 Unitary working units.
237

Chapter 9 Polynomials and Matrices 241
1 Polynomial .
241
2 Polynomials of matrices and linear mappings.
243

Chapter 10: Triangulation of Matrices and Linear Mappings 249
1 Existence of triangulation.
249
2 Hamilton-Cayley theorem.
253
3 Diagonalization of the unitary idea.
255

Chapter 11 Polynomials and Factorization 259
1 Euclid's algorithm.
259
2 Greatest common divisor.
262
3 Uniqueness of factorization.
265
4 Applications to decomposition of vector spaces.
270
5 Shure's Alemma.
274
6 Jordan's standard form..
276

Chapter 12 Convex Sets 283
1 Definition .
283
2 Separating hyperplanes.
285
3 poles and support hyperplanes.
288
4 Krain-Millman theorem.
289

Appendix 1 293 Complex Numbers.
293
Appendix 2 299 Iwasawa Decomposition and Other Topics.
299

Glossary of Terms (Alphabetical Order) 311

Glossary (alphabetical) 319

Search 327