Author: Dai Hua Editor-in-Chief: Dai Hua Editor-in-Chief Series Project: Postgraduate Mathematics Teaching Series Project: Paperback Edition 23cm/288 Publishing Project: Science Press/20065438+0 (reprinted in 2002) ISBN No. :70300967 * */o 156438+0.20000000 1
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Book Introduction-Matrix Theory
This book comprehensively and systematically introduces the basic theory, methods and some applications of matrix theory. The book is divided into 10 chapters, which introduce linear space and inner product space, linear mapping and linear transformation, λ matrix and Jordan canonical form, elementary matrix and matrix decomposition, Hermite matrix and positive definite matrix, norm theory and perturbation analysis, matrix function and matrix-valued function, generalized inverse matrix and linear equations, Kronecker product and linear matrix equations, nonnegative matrix and M matrix respectively. This book is rich in content and rigorous in discussion. There are a certain number of exercises at the back of each chapter, which is helpful for readers to learn and consolidate. This book can be used as a teaching material for graduate students and senior undergraduates in science and engineering colleges, and also as a reference book for teachers and engineers in related majors. Book Catalogue-Matrix Theory
Chapter 1 Linear Space and Inner Product Space
1. 1 Preparatory knowledge: set, mapping, number field
1. 1. 1 set and its operation
1. 1.2 binary relation and equivalence relation
1. 1.3 mapping
1. 1.4 number field and algebraic operation
1.2 linear space
1.2. 1 linear space and its basic properties
Linear correlation of 1.2.2 vector
1.2.3 Dimension of Linear Space
1.3 basis and coordinates
1.4 linear subspace
The concept of 1.4. 1 linear subspace
Intersection of 1.4.2 subspaces
Direct sum of 1.4.3 subspaces
Isomorphism of 1.5 linear space
1.6 internal product space
1.6. 1 inner product space and its basic properties
1.6.2 orthogonal basis and Gram-Schmidt orthogonalization method
1.6.3 orthogonal complementary projection theorem
utilize
Chapter II Linear Mapping and Linear Transformation
2. 1 Linear Mapping and Its Matrix Representation
2. Definition and properties of1.1linear mapping
2. The operation of1.2 linear mapping
2. Matrix Representation of1.3 Linear Mapping
2.2 Scope and Kernel of Linear Mapping
2.3 linear transformation
2.4 eigenvalues and eigenvectors
2.5 Similar Diagonal Form of Matrix
2.6 Invariant Subspace of Linear Transformation
2.7 unitary (orthogonal) transformation and unitary (orthogonal) matrix
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Chapter 3 λ matrix and Jordan canonical form of matrix
3. 1 unary polynomial
3.2λ matrix and its canonical form under offset
3.2. Basic concept of1λ matrix
3.2.2 Elementary Transformation and Offset of λ Matrix
3.2.3 Normal form of λ matrix under offset
Determinant factor and elementary factor of 3.3λ matrix
3.4 Conditions of Matrix Similarity
Jordan canonical form of 3.5 matrix
3.6 Kelley-Hamilton Theorem and Minimum Polynomial
utilize
Chapter 4 Factorization of Matrix
4. 1 elementary matrix
4. 1. 1 elementary matrix
4. 1.2 Elementary Lower Triangular Matrix
4. 1.3 Home Matrix
4.2 Full Rank Decomposition
4.3 Triangular Decomposition
4.4QR decomposition
4.5 Schur Theorem and Normal Matrix
4.6 Singular Value Decomposition
utilize
Chapter 5 Hermite Matrix and Positive Definite Matrix
5. 1 Hermite matrix and Hermite quadratic form
5. 1. 1 Hermite matrix
5. Inertia of1.2 Matrix
5. 1.3 Hermite quadratic form
5.2Hermite positive definite (nonnegative definite) matrix
5.3 Matrix Inequalities
* 5.4 Eigenvalues of Hermite Matrix
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Chapter VI Norms and Restrictions
6. 1 intermediate quantity quota
6.2 matrix specification
6.2. 1 Basic concepts
Compatibility matrix specification
Operator specification
6.3 Matrix sequence and matrix series
Limit of matrix sequence
Matrix series
6.4 matrix disturbance analysis
6.4. Inverse perturbation analysis of1matrix
6.4.2 Perturbation analysis of solutions of linear equations
6.4.3 matrix eigenvalue perturbation analysis
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Chapter 7 Matrix Functions and Matrix-valued Functions
7. 1 matrix function
7. Power series representation of1.1matrix function
7. Another Definition of1.2 Matrix Function
7.2 Matrix-valued function
7.2. 1 matrix-valued function
7.2.2 Analysis and operation of matrix-valued functions
7.3 Application of matrix-valued function in differential equation
7.4 Sensitivity Analysis of Feature Pairs *
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Chapter VIII Generalized Inverse Matrix
8. The concept of1generalized inverse matrix
8.2 Solutions of Generalized Inverse Matrix and Linear Equations
8.3 Minimum norm generalized inverse and minimum norm solution of linear equations
8.4 Least Square Solutions of Generalized Inverse and Contradictory Least Square Equations
8.5 Generalized Inverse Matrix and Least Square Solution of Linear Equations
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Chapter 9 Kronecker product and linear matrix equation
9. Kronecker product of1matrix
9.2 Straightening of Matrix and Linear Matrix Equations
Matrix straightening
Linear matrix equation
9.3 matrix equation AXB=C and matrix optimal approximation problem
9.3. 1 matrix equation
9.3.2 Best Approximation of Matrix with Constraints
9.4 Hermite solution of matrix equation AX=B and the best approximation of matrix
9.5 matrix equations AX+XB=C and X-AXB=C*
Matrix equation AX+XB=C
9.5.2 matrix equation X-AXB=C
utilize
Chapter 10 Nonnegative Matrix *
10. 1 nonnegative matrix and positive matrix
10.2 prime matrix and irreducible nonnegative matrix
10.2. 1 prime matrix
10.2.2 irreducible nonnegative matrix
10.3 random matrix
10.4m matrix
utilize
refer to
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