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1.

図書

図書
Per-Olov Löwdin and Quantum Theory Project, University of Florida
出版情報: New York : John Wiley & Sons, c1998  xi, 458 p. ; 25 cm
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2.

図書

図書
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1:
Real Numbers and Complex Numbers / 1.1:
Complex Series, Euler's Formula, and the Roots of Unity / 1.2:
Vector Spaces and Bases / 1.3:
Linear Transformations, Matrices, and Change of Basis / 1.4:
Diagonalization of Linear Transformations and Matrices / 1.5:
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6:
The Discrete Fourier Transform / 2:
Basic Properties of the Discrete Fourier Transform / 2.1:
Translation-Invariant Linear Transformations / 2.2:
The Fast Fourier Transform / 2.3:
Wavelets on $bZ_N$ / 3:
Construction of Wavelets on $bZ_N$: The First Stage / 3.1:
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2:
Examples and Applications / 3.3:
Wavelets on $bZ$ / 4:
$ ell ^2(bZ)$ / 4.1:
Complete Orthonormal Sets in Hilbert Spaces / 4.2:
$L^2([- pi , pi ))$ and Fourier Series / 4.3:
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4:
First-Stage Wavelets on $bZ$ / 4.5:
The Iteration Step for Wavelets on $bZ$ / 4.6:
Implementation and Examples / 4.7:
Wavelets on $bR$ / 5:
$L^2(bR)$ and Approximate Identities / 5.1:
The Fourier Transform on $bR$ / 5.2:
Multiresolution Analysis and Wavelets / 5.3:
Construction of Multiresolution Analyses / 5.4:
Wavelets with Compact Support and Their Computation / 5.5:
Wavelets and Differential Equations / 6:
The Condition Number of a Matrix / 6.1:
Finite Difference Methods for Differential Equations / 6.2:
Wavelet-Galerkin Methods for Differential Equations / 6.3:
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
3.

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
4.

図書

図書
Paul A. Fuhrmann
出版情報: New York ; Tokyo : Springer, c1996  xiii, 360 p. ; 24 cm
シリーズ名: Universitext
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5.

図書

図書
V.V. Prasolov ; [translated by D.A. Leites from an original Russian manuscript ; translation edited by Simeon Ivanov]
出版情報: Providence, R.I. : American Mathematical Society, c1994  xviii, 225 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 134
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Main notations and conventions
Determinants Linear spaces
Canonical forms of matrices and linear operators
Matrices of special form Multilinear algebra
Matrix inequalities
Matrices in algebra and calculus
Appendix
Bibliography
Subject Index
Main notations and conventions
Determinants Linear spaces
Canonical forms of matrices and linear operators
6.

図書

図書
William C. Brown
出版情報: New York : M. Dekker, c1991  viii, 309 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 145
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7.

図書

図書
edited by D.G. Corneil and R. Mathon
出版情報: Boston ; Tokyo : Academic Press, c1991  xix, 410 p. ; 24 cm
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8.

図書

図書
Thomas Banchoff, John Wermer
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xii, 305 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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9.

図書

図書
Philip E. Gill, Walter Murray, Margaret H. Wright
出版情報: Redwood City, Calif. : Addison-Wesley Pub. Co., Advanced Book Program, c1991  xvii, 426 p. ; 24 cm
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10.

図書

図書
T.S. Blyth
出版情報: Oxford [England] : Clarendon Press , New York : Oxford University Press, 1990  vi, 360 p. ; 24 cm
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Modules, Vector Spaces and Algebras / 1:
Submodules; Intersections and Sums / 2:
Morphisms; Exact Sequences / 3:
Quotient Modules; Basic Isomorphism Theorems / 4:
Chain Conditions; Jordan-Holder Towers / 5:
Products and Coproducts / 6:
Free Modules; Bases / 7:
Groups of Morphisms; Projective Modules / 8:
Duality; Transposition / 9:
Matrices; Linear Equations / 10:
Inner Product Spaces / 11:
Injective Modules / 12:
Simple and Semisimple Modules / 13:
The Jacobson Radical / 14:
Tensor Products; Flat Modules; Regular Rings / 15:
Tensor Products; Tensor Algebras / 16:
Exterior Algebras, Determinants / 17:
Modules Over A Principal Ideal Domain; Finitely Generated Abelian Groups / 18:
Vector Space Decomposition Theorems; Canonical Forms Under Similarity / 19:
Diagonalisation; Normal Transformations / 20:
Modules, Vector Spaces and Algebras / 1:
Submodules; Intersections and Sums / 2:
Morphisms; Exact Sequences / 3:
11.

図書

図書
Morton L. Curtis ; with revisions by Paul Place
出版情報: New York : Springer-Verlag, c1990  x, 168 p. ; 24 cm
シリーズ名: Universitext
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Algebraic Preliminaries
Vector Spaces and Linear Maps
Matrices and Determinants
Rings and Polynomials
Inner Product Spaces
Normed Algebras
Bibliography
Index
Algebraic Preliminaries
Vector Spaces and Linear Maps
Matrices and Determinants
12.

図書

図書
Adam Ostaszewski
出版情報: Cambridge ; New York : Cambridge University Press, 1990  xiii, 545 p. ; 23 cm
シリーズ名: LSE mathematical series
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目次情報: 続きを見る
Preface
Linear Algebra / Part I:
Vector spaces (revision) / 1:
Geometry in R / 2:
Matrices / 3:
Projections / 4:
Spectral theory / 5:
The upper triangular form / 6:
The tri-diagonal form / 7:
Inverses / 8:
Convexity / 9:
The separating hyperplane theorem / 10:
Linear inequalities / 11:
Linear programming and game theory / 12:
The simplex method / 13:
Partial derivatives (revision) / 14:
Convex functions / 15:
Non-linear programming / 16:
Advanced Calculus / Part II:
The integration process
Manipulation of integrals
Multiple integrals
Differential and difference equations (revision)
Laplace transforms
Series solutions of differential equations
Calculus of variations
Solutions to Selected Exercises / Part III:
Index
Preface
Linear Algebra / Part I:
Vector spaces (revision) / 1:
13.

図書

図書
S.K. Godunov ; [translator, Tamara Rozhkovskaya with the participation of Scientific Books (RIMIBE NSU), Novosibirsk, Russia]
出版情報: Providence, R.I. : American Mathematical Society, c1998  xvi, 303 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 175
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14.

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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目次情報: 続きを見る
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:
15.

図書

図書
Steven Roman
出版情報: New York ; Tokyo : Springer-Verlag, c1992  xii, 363 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 135
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16.

図書

図書
Larry Smith
出版情報: New York : Springer, c1998  xii, 452 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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17.

図書

図書
Rami Shakarchi
出版情報: New York ; Tokyo : Springer-Verlag, c1996  xi, 183 p. ; 24 cm
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目次情報: 続きを見る
Vector Spaces
Matrices
Linear Mappings
Linear Maps and Matrices
Scalar Products and Orthogonality
Determinants
Symmetric, Hermitian, and Unitary Operators
Eigenvectors and Eigenvalues
Polynomials and Matrices
Triangulation of Matrices and Linear Maps
Polynomials and Primary Decomposition
Convex Sets
Vector Spaces
Matrices
Linear Mappings
18.

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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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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