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1.

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
2.

図書

図書
Gilbert Strang
出版情報: Wellesley, Mass. : Wellesley-Cambridge Press, c2016  x, 574 p. ; 24 cm
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目次情報: 続きを見る
Introduction to Vectors / 1:
Vectors and Linear Combinations / 1.1:
Lengths and Dot Products / 1.2:
Matrices / 1.3:
Solving Linear Equations / 2:
Vectors and Linear Equations / 2.1:
The Idea of Elimination / 2.2:
Elimination Using Matrices / 2.3:
Rules for Matrix Operations / 2.4:
Inverse Matrices / 2.5:
Elimination = Factorization: A = LU / 2.6:
Transposes and Permutations / 2.7:
Vector Spaces and Subspaces / 3:
Spaces of Vectors / 3.1:
The Nullspace of A: Solving Ax = 0 and Rx = 0 / 3.2:
The Complete Solution to Ax = b / 3.3:
Independence, Basis and Dimension / 3.4:
Dimensions of the Four Subspaces / 3.5:
Orthogonality / 4:
Orthogonality of the Four Subspaces / 4.1:
Projections / 4.2:
Least Squares Approximations / 4.3:
Orthonormal Bases and Gram-Schmidt / 4.4:
Determinants / 5:
The Properties of Determinants / 5.1:
Permutations and Cofactors / 5.2:
Cramer's Rule, Inverses, and Volumes / 5.3:
Eigenvalues and Eigenvectors / 6:
Introduction to Eigenvalues / 6.1:
Diagonalizing a Matrix / 6.2:
Systems of Differential Equations / 6.3:
Symmetric Matrices / 6.4:
Positive Definite Matrices / 6.5:
The Singular Value Decomposition (SVD) / 7:
Image Processing by Linear Algebra / 7.1:
Bases and Matrices in the SVD / 7.2:
Principal Component Analysis (PCA by the SVD) / 7.3:
The Geometry of the SVD / 7.4:
Linear Transformations / 8:
The Idea of a Linear Transformation / 8.1:
The Matrix of a Linear Transformation / 8.2:
The Search for a Good Basis / 8.3:
Complex Vectors and Matrices / 9:
Complex Numbers / 9.1:
Hermitian and Unitary Matrices / 9.2:
The Fast Fourier Transform / 9.3:
Applications / 10:
Graphs and Networks / 10.1:
Matrices in Engineering / 10.2:
Markov Matrices, Population, and Economics / 10.3:
Linear Programming / 10.4:
Fourier Series: Linear Algebra for Functions / 10.5:
Computer Graphics / 10.6:
Linear Algebra for Cryptography / 10.7:
Numerical Linear Algebra / 11:
Gaussian Elimination in Practice / 11.1:
Norms and Condition Numbers / 11.2:
Iterative Methods and Preconditioned / 11.3:
Linear Algebra in Probability & Statistics / 12:
Mean, Variance, and Probability / 12.1:
Covariance Matrices and Joint Probabilities / 12.2:
Multivariate Gaussian and Weighted Least Squares / 12.3:
Matrix Factorizations
Index
Sex Great Theorems/Linear Algebra in a Nutshell
Introduction to Vectors / 1:
Vectors and Linear Combinations / 1.1:
Lengths and Dot Products / 1.2:
3.

図書

図書
[by] Evar D. Nering
出版情報: New York : Wiley, c1970  xii, 352 p. ; 23 cm
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目次情報: 続きを見る
Introduction
Vector Spaces
Linear Transformations and Matrics
Determinants, Eigenvalues, and Similarity Transformations
Linear Functionals, Bilinear Forms, Quadratic Forms
Orthogonal and Unitary Transformations, Normal Matrices
Selected Applications of Linear Algebra
Appendix
Answers to Selected Exercises
Introduction
Vector Spaces
Linear Transformations and Matrics
4.

図書

図書
translated from the Russian by Richard A. Silverman
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, 1961  310 p. ; 24 cm
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5.

図書

図書
Daniel Pedoe
出版情報: Bronx, N.Y. : Chelsea Pub. Co., c1976  xi, 226 p. ; 24 cm
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6.

図書

図書
Stanley I. Grossman
出版情報: Orlando ; Tokyo : Academic Press, c1986  xiv, 876, 92, 10 p. ; 26 cm
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7.

図書

図書
A. Wayne Roberts
出版情報: Reading, Mass. : Benjamin/Cummings Pub. Co., c1985  xv, 414 p. ; 25 cm
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8.

図書

図書
R.E. Kalman, P.L. Falb, M.A. Arbib
出版情報: New York : McGraw-Hill, c1969  xiv, 358 p. ; 23 cm
シリーズ名: International series in pure and applied mathematics
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9.

図書

図書
Frank M. Stewart
出版情報: Princeton, N.J. : Van Nostrand, c1963  xv, 281 p. ; 24 cm
シリーズ名: The university series in undergraduate mathematics
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10.

図書

図書
Richard S. Palais
出版情報: New York : W.A. Benjamin, 1968  vii, 131 p. ; 28 cm
シリーズ名: Mathematics lecture note series
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11.

図書

図書
Hans Blomberg and Raimo Ylinen
出版情報: London ; New York : Academic Press, 1983  xx, 360 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 166
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12.

図書

図書
W. Murray Wonham
出版情報: New York : Springer-Verlag, c1979  xv, 326 p. ; 25 cm
シリーズ名: Applications of mathematics ; 10
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13.

図書

図書
T. S. Blyth
出版情報: Oxford [Eng.] : Clarendon Press, 1977  vi, 400 p. ; 24 cm
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目次情報: 続きを見る
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:
14.

図書

図書
William F. Trench and Bernard Kolman
出版情報: New York : Academic Press, c1972  xi, 758 p. ; 25 cm
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