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1.

図書

図書
Denis Serre
出版情報: New York ; Tokyo : Springer, c2002  xv, 202 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 216
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Preface
List of Symbols
Elementary Theory / 1:
Basics / 1.1:
Change of Basis / 1.2:
Exercises / 1.3:
Square Matrices / 2:
Determinants and Minors / 2.1:
Invertibility / 2.2:
Alternate Matrices and the Pfaffian / 2.3:
Eigenvalues and Eigenvectors / 2.4:
The Characteristic Polynomial / 2.5:
Diagonalization / 2.6:
Trigonalization / 2.7:
Irreducibility / 2.8:
Matrices with Real or Complex Entries / 2.9:
Eigenvalues of Real- and Complex-Valued Matrices / 3.1:
Spectral Decomposition of Normal Matrices / 3.2:
Normal and Symmetric Real-Valued Matrices / 3.3:
The Spectrum and the Diagonal of Hermitian Matrices / 3.4:
Norms / 3.5:
A Brief Review / 4.1:
Householder's Theorem / 4.2:
An Interpolation Inequality / 4.3:
A Lemma about Banach Algebras / 4.4:
The Gershgorin Domain / 4.5:
Nonnegative Matrices / 4.6:
Nonnegative Vectors and Matrices / 5.1:
The Perron-Frobenius Theorem: Weak Form / 5.2:
The Perron-Frobenius Theorem: Strong Form / 5.3:
Cyclic Matrices / 5.4:
Stochastic Matrices / 5.5:
Matrices with Entries in a Principal Ideal Domain; Jordan Reduction / 5.6:
Rings, Principal Ideal Domains / 6.1:
Invariant Factors of a Matrix / 6.2:
Similarity Invariants and Jordan Reduction / 6.3:
Exponential of a Matrix, Polar Decomposition, and Classical Groups / 6.4:
The Polar Decomposition / 7.1:
Exponential of a Matrix / 7.2:
Structure of Classical Groups / 7.3:
The Groups U(p,q) / 7.4:
The Orthogonal Groups O(p,q) / 7.5:
The Symplectic Group Spn / 7.6:
Singular Value Decomposition / 7.7:
Matrix Factorizations / 7.8:
The LU Factorization / 8.1:
Choleski Factorization / 8.2:
The QR Factorization / 8.3:
The Moore-Penrose Generalized Inverse / 8.4:
Iterative Methods for Linear Problems / 8.5:
A Convergence Criterion / 9.1:
Basic Methods / 9.2:
Two Cases of Convergence / 9.3:
The Tridiagonal Case / 9.4:
The Method of the Conjugate Gradient / 9.5:
Approximation of Eigenvalues / 9.6:
Hessenberg Matrices / 10.1:
The QR Method / 10.2:
The Jacobi Method / 10.3:
The Power Methods / 10.4:
Leverrier's Method / 10.5:
References / 10.6:
Index
Preface
List of Symbols
Elementary Theory / 1:
2.

図書

図書
by J.H.M. Wedderburn
出版情報: Ann Arbor, Mich. : Cushing-Malloy, 1960  vii, 205 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 17
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3.

図書

図書
James R. Schott
出版情報: Hoboken, N.J. : John Wiley, c2005  xiii, 456 p. ; 25 cm
シリーズ名: Wiley series in probability and mathematical statistics
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目次情報: 続きを見る
Preface
A Review of Elementary Matrix Algebra / 1:
Vector Spaces / 2:
Eigenvalues and Eigenvectors / 3:
Matrix Factorizations and Martrix Norms / 4:
Generalized Inverses / 5:
Systems of Linear Equations / 6:
Partitioned Matrices / 7:
Special Matrices and Matrix Operations / 8:
Matrix Derivatives and Related Topics / 9:
Some Special Topics Related to Quadratic Forms / 10:
References
Index
Preface
A Review of Elementary Matrix Algebra / 1:
Vector Spaces / 2:
4.

図書

図書
Jan R. Magnus and Heinz Neudecker
出版情報: Chichester ; New York : Wiley, c1999  xviii, 395 p. ; 24 cm
シリーズ名: Wiley series in probability and mathematical statistics ; . Applied probability and statistics
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Matrices: Basic Properties of Vectors and Matrices
Kronecker Products, the Vec Operator and the Moore-Penrose Inverse
Miscellaneous Matrix Results
Differentials: The Theory: Mathematical Preliminaries
Differentials and Differentiability
The Second Differential
Static Optimization
Differentials: The Practice: Some Important Differentials
First Order Differentials and Jacobian Matrices
Second Order Differentials and Hessian Matrices
Inequalities: Inequalities
The Linear Model: Statistical Preliminaries
The Linear Regression Model
Further Topics in the Linear Model
Applications to Maximum Likelihood Estimation: Maximum Likelihood Estimation
Simultaneous Equations
Topics in Psychometrics
Matrices: Basic Properties of Vectors and Matrices
Kronecker Products, the Vec Operator and the Moore-Penrose Inverse
Miscellaneous Matrix Results
5.

図書

図書
by Daniel T. Finkbeiner, II ; drawings by Evan Gillespie
出版情報: San Francisco : W.H. Freeman , Tokyo : Charles E. Tuttle, 1960  vii, 248 p.: ill. ; 22 cm
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6.

図書

図書
A.M. Mathai
出版情報: Singapore ; New Jersey : World Scientific, c1997  xii, 435 p. ; 23 cm
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7.

図書

図書
von Rudolf Zurmühl
出版情報: Berlin : Springer, 1964  xii, 452 p. ; 24 cm
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8.

図書

図書
by Hans Schwerdtfeger
出版情報: Groningen : P. Noordhoff, 1950  279 p. ; 25 cm
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9.

図書

図書
Carl Meyer
出版情報: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000  2 v. ; 25 cm.
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目次情報: 続きを見る
Preface
Linear Equations / 1.:
Introduction / 1.1:
Gaussian Elimination and Matrices / 1.2:
Gauss-Jordan Method / 1.3:
Two-Point Boundary Value Problems / 1.4:
Making Gaussian Elimination Work / 1.5:
Ill-Conditioned Systems / 1.6:
Rectangular Systems and Echelon Forms / 2.:
Row Echelon Form and Rank / 2.1:
Reduced Row Echelon Form / 2.2:
Consistency of Linear Systems / 2.3:
Homogeneous Systems / 2.4:
Nonhomogeneous Systems / 2.5:
Electrical Circuits / 2.6:
Matrix Algebra / 3.:
From Ancient China to Arthur Cayley / 3.1:
Addition and Transposition / 3.2:
Linearity / 3.3:
Why Do It This Way / 3.4:
Matrix Multiplication / 3.5:
Properties of Matrix Multiplication / 3.6:
Matrix Inversion / 3.7:
Inverses of Sums and Sensitivity / 3.8:
Elementary Matrices and Equivalence / 3.9:
The LU Factorization / 3.10:
Vector Spaces / 4.:
Spaces and Subspaces / 4.1:
Four Fundamental Subspaces / 4.2:
Linear Independence / 4.3:
Basis and Dimension / 4.4:
More about Rank / 4.5:
Classical Least Squares / 4.6:
Linear Transformations / 4.7:
Change of Basis and Similarity / 4.8:
Invariant Subspaces / 4.9:
Norms, Inner Products, and Orthogonality / 5.:
Vector Norms / 5.1:
Matrix Norms / 5.2:
Inner-Product Spaces / 5.3:
Orthogonal Vectors / 5.4:
Gram-Schmidt Procedure / 5.5:
Unitary and Orthogonal Matrices / 5.6:
Orthogonal Reduction / 5.7:
Discrete Fourier Transform / 5.8:
Complementary Subspaces / 5.9:
Range-Nullspace Decomposition / 5.10:
Orthogonal Decomposition / 5.11:
Singular Value Decomposition / 5.12:
Orthogonal Projection / 5.13:
Why Least Squares? / 5.14:
Angles between Subspaces / 5.15:
Determinants / 6.:
Additional Properties of Determinants / 6.1:
Eigenvalues and Eigenvectors / 7.:
Elementary Properties of Eigensystems / 7.1:
Diagonalization by Similarity Transformations / 7.2:
Functions of Diagonalizable Matrices / 7.3:
Systems of Differential Equations / 7.4:
Normal Matrices / 7.5:
Positive Definite Matrices / 7.6:
Nilpotent Matrices and Jordan Structure / 7.7:
Jordan Form / 7.8:
Functions of Nondiagonalizable Matrices / 7.9:
Difference Equations, Limits, and Summability / 7.10:
Minimum Polynomials and Krylov Methods / 7.11:
Perron-Frobenius Theory / 8.:
Positive Matrices / 8.1:
Nonnegative Matrices / 8.3:
Stochastic Matrices and Markov Chains / 8.4:
Index
Preface
Linear Equations / 1.:
Introduction / 1.1:
10.

図書

図書
Allan Pinkus
出版情報: New York : Cambridge University Press, 2010  xi, 182 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 181
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Foreword
Basic properties of totally positive matrices / 1:
Criteria for total positivity and strict total positivity / 2:
Variation diminishing / 3:
Examples / 4:
Eigenvalues and eigenvectors / 5:
Factorizations of totally positive matrices / 6:
Afterword
References
Subject index
Author index
Foreword
Basic properties of totally positive matrices / 1:
Criteria for total positivity and strict total positivity / 2:
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