发帖
雷达卡
名称：matrix analysis
大小：561页
目录：
0.Review and miscellanea
Introduction
Vector spaces
Matrices
Determinants
Rank
Nonsingularity
The usual inner product
Partitioned matrices
Determinants again
Special types of matrices
Change of basis
1.Eigenvalues, eigenvectors, and similarity
1.0 Introduction
1.1 The eigenvalue-eigenvector equation
1.2 The characteristic polynomial
1.3 Similarity
1.4 Eigenvectors
2 Unitary equivalence and normal matrices
2.0 Introduction
2.1 Unitary matrices
2.2 Unitary equivalence
2.3 Schur's unitary triangularization theorem
2.4 Some implications of Schur's theorem
2.5 Normal matrices
2.6 QR factorization and algorithm
3 Canonical forms
3.0 Introduction
3.1 The Jordan canonical form: a proof
3.2 The Jordan canonical form: some observations
and applications
3.3 Polynomials and matrices: the minimal
polynomial
3.4 Other canonical forms and factorizations
3.5 Triangular factorizations
4 Hermitian and symmetric matrices
4.0 Introduction
4.1 Definitions, properties, and characterizations of
Hermitian matrices
4.2 Variational characterizations of eigenvalues of
Hermitian matrices
4.3 Some applications of the variational
characterizations
4.4 Complex symmetric matrices
4.5 Congruence and simultaneous diagonalization
of Hermitian and symmetric matrices
4.6 Consimilarity and condiagonalization
5.0 Norms for vectors and matrices
5.1 Introduction
5.1Defining properties of vector norms and inner
products
5.2Examples of vector norms
5.3Algebraic properties of vector norms
5.4Analytic properties of vector norms
5.5Geometric properties of vector norms
5.6Matrix norms
5.7Vector norms on matrices
5.8Errors in inverses and solutions of linear
systems
6 Location and perturbation of eigenvalues
6.0 Introduction
6.1 Gerggorin discs
6.2 Gerigorin discs - a closer look
6.3 Perturbation theorems
6.4 Other inclusion regions
7 Positive definite matrices
7.0 Introduction
7.1 Definitions and properties
7.2 Characterizations
7.3 The polar form and the singular value
decomposition
7.4 Examples and applications of the singular value
decomposition
7.5 The Schur product theorem
7.6 Congruence: products and simultaneous
diagonalization
7.7 The positive semidefinite ordering
7.8 Inequalities for positive definite matrices
8 Nonnegative matrices
8.0 Introduction
8.1 Nonnegative matrices - inequalities and
generalities
8.2 Positive matrices
8.3 Nonnegative matrices
8.4 Irreducible nonnegative matrices
8.5 Primitive matrices
8.6 A general limit theorem
8.7 Stochastic and doubly stochastic matrices
Appendices
A Complex numbers
B Convex sets and functions
C The fundamental theorem of algebra
D Continuous dependence of the zeroes of a
polynomial on its coefficients
E Weierstrass's theorem
References
Notation
Index
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