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図書

図書
Peter D. Lax
出版情報: New York : John Wiley, c1997  xiv, 250 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Fundamentals
Duality
Linear Mappings
Matrices
Determinant and Trace
Spectral Theory
Euclidean Structure
Spectral Theory of Selfadjoint Mappings
Calculus of Vector and Matrix Valued Functions
Matrix Inequalities
Kinematics and Dynamics
Convexity
The Duality Theorem
Normed Linear Spaces
Linear Mappings Between Normed Spaces
Positive Matrices
How to Solve Systems of Linear Equations
Appendices
Bibliography
Index
List of Series Titles
Fundamentals
Duality
Linear Mappings
2.

図書

図書
Lloyd N. Trefethen, David Bau, III
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, c1997  xii, 361 p. ; 26 cm
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Preface
Fundamental: / Part I:
Matrix-vector multiplication / 1:
Orthogonal vectors and matrices / 2:
Norms / 3:
The singular value decomposition / 4:
More on the SVD / 5:
QR Factorization and Least Squares: / Part II:
Projectors / 6:
QR factorization / 7:
Gram-Schmidt orthogonalization / 8:
MATLAB / 9:
Householder triangularization / 10:
Least squares problems / 11:
Conditioning and Stability: / Part III:
Conditioning and condition numbers / 12:
Floating point arithmetic / 13:
Stability / 14:
More on stability / 15:
Stability of householder triangularization / 16:
Stability of back substitution / 17:
Conditioning of least squares problems / 18:
Stability of least squares algorithms / 19:
Systems of Equations: / Part IV:
Gaussian elimination / 20:
Pivoting / 21:
Stability of Gaussian elimination / 22:
Cholesky factorization / 23:
Eigenvalues: / Part V:
Eigenvalue problems / 24:
Overview of Eigenvalue algorithms / 25:
Reduction to Hessenberg or tridiagonal form / 26:
Rayleigh quotient, inverse iteration / 27:
QR algorithm without shifts / 28:
QR algorithm with shifts / 29:
Other Eigenvalue algorithms / 30:
Computing the SVD / 31:
Iterative Methods: / Part VI:
Overview of iterative methods / 32:
The Arnoldi iteration / 33:
How Arnoldi locates Eigenvalues / 34:
GMRES / 35:
The Lanczos iteration / 36:
From Lanczos to Gauss quadrature / 37:
Conjugate gradients / 38:
Biorthogonalization methods / 39:
Preconditioning / 40:
Appendix
Notes
Bibliography
Index
Preface
Fundamental: / Part I:
Matrix-vector multiplication / 1:
3.

図書

図書
Bernard Kolman with the assistance of David R. Hill
出版情報: Upper Saddle River, N.J. : Prentice Hall, c1997  xvii, 608, 70, 8 p. ; 25 cm
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目次情報: 続きを見る
Introductory Linear Algebra / I:
Linear Equations and Matrices / 1:
Linear Systems
Matrices
Dot Product and Matrix Multiplication
Properties of Matrix Operations
Graph Theory (Optional)
Solutions of Linear Systems of Equations
Electrical Circuits (Optional)
Markov Chains (Optional)
The Inverse of a Matrix
Linear Economic Models (Optional)
Wavelets (Optional)
LU-Factorization (Optional)
Determinants / 2:
Definition and Properties
Cofactor Expansion and Applications
Determinants from a Computational Point of View
Vectors in R2 and R3 / 3:
Vectors in the Plane
N-Vectors
Introduction to Linear Transformations
Computer Graphics
Computer Graphics (Optional)
Cross Products in R3 (Optional)
Lines and Planes
Real Vector Spaces / 4:
Subspaces
Linear Independence
Basis and Dimension
Homogeneous Systems
The Rank of a Matrix and Applications
Coordinates and Change of Basis
Orthonormal Bases in Rn
QR-Factorization (Optional)
Orthogonal Complements
Least Squares (Optional)
Eigenvalues and Eigenvectors / 5:
Diagonalization and Similar Matrices
Diagonalization and Symmetric Matrices
Linear Transformations and Matrices / 6:
Definition and Examples
The Kernel and Range of a Linear Transformation
The Matrix of a Linear Transformation
Cumulative Review of Part I
OTHER APPLICATIONS / II:
Linear Programming / 7:
The Linear Programming Problem
Geometric Solution
The Simplex Method
Duality
The Theory of Games
Applications of Eigenvalues and Eigenvectors / 8:
The Fibonacci Sequence
Differential Equations (Calculus Required)
Dynamical Systems (Calculus Required)
Intro to Fractals
Quadratic Forms
Conic Sections
Quadric Surfaces
Introduction to MATLAB / Appendix A:
Complex Numbers / Appendix B:
Complex Numbers in Linear Algebra
Further Directions / Appendix C:
Inner Product Spaces (Calculus Required)
Composite and Invertible Linear Transformations
Answers to Odd-Numbered Exercises and Chapter Tests
Index
Introductory Linear Algebra / I:
Linear Equations and Matrices / 1:
Linear Systems
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