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1.

図書
図書
1. Matrix analysis and applied linear algebra (: set ; [main] ; solutions manual)
Carl Meyer
出版情報: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000  2 v. ; 25 cm.
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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：
2.

図書
図書
2. Elementary linear algebra : applications version. 8th ed
Howard Anton, Chris Rorres
出版情報: New York : John Wiley, c2000  xvi, [8], 822 p. ; 27 cm
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Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
Vectors in 2-Space and 3-Space / 1：
Linear Equations and Matrices
Euclidean Vector Spaces
Systems of Linear Equations
General Vector Spaces
Matrices
Inner Product Spaces
Matrix Multiplication
Eigenvalues, Eigenvectors
Algebraic Properties of Matrix Operations
Linear Transformations
Special Types of Matrices and Partitioned Matrices
Additional Topics
Matrix Transformations
Complex Vector Spaces
Computer Graphics
Answers to Exercises
Correlation Coefficient (Optional)
Photo Credits
Index / 2：
Solving Linear Systems
Echelon Form of a Matrix
Elementary Matrices: Finding A-1
Equivalent Matrices
LU-Factorization (Optional)
Real Vector Spaces / 3：
Vectors in the Plane and in 3-space
Vector Spaces
Subspaces
Span and Linear Independence
Basis and Dimension
Homogeneous Systems
Coordinates and Isomorphisms
Rank of a Matrix
Standard Inner Product on R2 and R3 / 4：
Cross Product in R3 (Optional)
Gram-Schmidt Process
Orthogonal Complements
Least Squares (Optional)
Linear Transformations and Matrices / 5：
Definition and Examples
Kernel and Range of a Linear Transformation
Matrix of a Linear Transformation
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)
Similarity
Inroduction to Homogeneous Coordinates (Optional)
Definition / 6：
Properties of Determinants
Cofactor Expansion
Inverse of a Matrix
Other Applications of Determinants
Determinants from a Computational Point of View
Eigenvalues and Eigenvectors / 7：
Diagonalization and Similar Matrices
Stable Age Distribution in a Population
Markov Processes (Optional)
Diagonalization of Symmetric Matrices
Spectral Decomposition and Singular Value Decomposition (Optional)
Real Quadratic Forms
Conic Sections
Quadric Surfaces
Dominant Eigenvalue and Principal Component Analysis (Optional)
Differential Equations (Optional) / 8：
Differential Equations
Dynamical Systems
MATLAB for Linear Algebra / 9：
Input and Output in MATLAB
Matrix Operations in MATLAB
Matrix Powers and Some Special Matrices
Elementary Row Operations in MATLAB
Matrix Inverses in MATLAB
Vectors in MATLAB
Applications of Linear Combinations in MATLAB
Linear Transformations in MATLAB
MATLAB Command Summary
MATLAB Exercises / 10：
Preliminaries Sets Functions / Appendix A：
Complex Numbers Complex Numbers Complex Numbers in Linear Algebra / Appendix B：
Introduction to Proofs / Appendix C：
Answers to Odd-Numbered Exercises
Systems of Linear Equations and Matrices
Note: All relevant chapters end with Supplementary Exercises.
Determinants
3.

図書
図書
3. The geometry of spacetime : an introduction to special and general relativity
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
4.

図書
図書
4. Differential equations, dynamical systems, and an introduction to chaos. 2nd ed
Morris W. Hirsch, Stephen Smale, Robert L. Devaney
出版情報: San Diego ; Tokyo : Elsevier Academic Press, c2004  xiv, 417 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 60
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Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
The Logistic Population Model / 1.2：
Constant Harvesting and Bifurcations / 1.3：
Periodic Harvesting and Periodic Solutions / 1.4：
Computing the Poincare Map / 1.5：
Exploration: A Two-Parameter Family / 1.6：
Planar Linear Systems / Chapter 2：
Second-Order Differential Equations / 2.1：
Planar Systems / 2.2：
Preliminaries from Algebra / 2.3：
Eigenvalues and Eigenvectors / 2.4：
Solving Linear Systems / 2.6：
The Linearity Principle / 2.7：
Phase Portraits for Planar Systems / Chapter 3：
Real Distinct Eigenvalues / 3.1：
Complex Eigenvalues / 3.2：
Repeated Eigenvalues / 3.3：
Changing Coordinates / 3.4：
Classification of Planar Systems / Chapter 4：
The Trace-Determinant Plane / 4.1：
Dynamical Classification / 4.2：
Exploration: A 3D Parameter Space / 4.3：
Higher Dimensional Linear Algebra / Chapter 5：
Preliminaries from Linear Algebra / 5.1：
Bases and Subspaces / 5.2：
Genericity / 5.5：
Higher Dimensional Linear Systems / Chapter 6：
Distinct Eigenvalues / 6.1：
Harmonic Oscillators / 6.2：
The Exponential of a Matrix / 6.3：
Nonautonomous Linear Systems / 6.5：
Nonlinear Systems / Chapter 7：
Dynamical Systems / 7.1：
The Existence and Uniqueness Theorem / 7.2：
Continuous Dependence of Solutions / 7.3：
The Variational Equation / 7.4：
Exploration: Numerical Methods / 7.5：
Equilibria in Nonlinear Systems / Chapter 8：
Some Illustrative Examples / 8.1：
Nonlinear Sinks and Sources / 8.2：
Saddles / 8.3：
Stability / 8.4：
Bifurcations / 8.5：
Exploration: Complex Vector Fields / 8.6：
Global Nonlinear Techniques / Chapter 9：
Nullclines / 9.1：
Stability of Equilibria / 9.2：
Gradient Systems / 9.3：
Hamiltonian Systems / 9.4：
Exploration: The Pendulum with Constant Forcing / 9.5：
Closed Orbits and Limit Sets / Chapter 10：
Limit Sets / 10.1：
Local Sections and Flow Boxes / 10.2：
The Poincare Map / 10.3：
Monotone Sequences in Planar Dynamical Systems / 10.4：
The Poincare-Bendixson Theorem / 10.5：
Applications of Poincare-Bendixson / 10.6：
Exploration: Chemical Reactions That Oscillate / 10.7：
Applications in Biology / Chapter 11：
Infectious Diseases / 11.1：
Predator/Prey Systems / 11.2：
Competitive Species / 11.3：
Exploration: Competition and Harvesting / 11.4：
Applications in Circuit Theory / Chapter 12：
An RLC Circuit / 12.1：
The Lienard Equation / 12.2：
The van der Pol Equation / 12.3：
A Hopf Bifurcation / 12.4：
Exploration: Neurodynamics / 12.5：
Applications in Mechanics / Chapter 13：
Newton's Second Law / 13.1：
Conservative Systems / 13.2：
Central Force Fields / 13.3：
The Newtonian Central Force System / 13.4：
Kepler's First Law / 13.5：
The Two-Body Problem / 13.6：
Blowing Up the Singularity / 13.7：
Exploration: Other Central Force Problems / 13.8：
Exploration: Classical Limits of Quantum Mechanical Systems / 13.9：
The Lorenz System / Chapter 14：
Introduction to the Lorenz System / 14.1：
Elementary Properties of the Lorenz System / 14.2：
The Lorenz Attractor / 14.3：
A Model for the Lorenz Attractor / 14.4：
The Chaotic Attractor / 14.5：
Exploration: The Rossler Attractor / 14.6：
Discrete Dynamical Systems / Chapter 15：
Introduction to Discrete Dynamical Systems / 15.1：
The Discrete Logistic Model / 15.2：
Chaos / 15.4：
Symbolic Dynamics / 15.5：
The Shift Map / 15.6：
The Cantor Middle-Thirds Set / 15.7：
Exploration: Cubic Chaos / 15.8：
Exploration: The Orbit Diagram / 15.9：
Homoclinic Phenomena / Chapter 16：
The Shil'nikov System / 16.1：
The Horseshoe Map / 16.2：
The Double Scroll Attractor / 16.3：
Homoclinic Bifurcations / 16.4：
Exploration: The Chua Circuit / 16.5：
Existence and Uniqueness Revisited / Chapter 17：
Proof of Existence and Uniqueness / 17.1：
Continuous Dependence on Initial Conditions / 17.3：
Extending Solutions / 17.4：
Nonautonomous Systems / 17.5：
Differentiability of the Flow / 17.6：
Bibliography
Index
Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
5.

図書
図書
5. Linear algebra and its applications. 2nd ed, update (: International ed.)
David C. Lay
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c2000  xx, 486, 57, 12 p. ; 24 cm
シリーズ名: Addison-Wesley world student series
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Linear Equations in Linear Algebra / 1：
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations / 1.1：
Row Reduction and Echelon Forms / 1.2：
Vector Equations / 1.3：
The Matrix Equation Ax = b / 1.4：
Solution Sets of Linear Systems / 1.5：
Applications of Linear Systems / 1.6：
Linear Independence / 1.7：
Introduction to Linear Transformations / 1.8：
The Matrix of a Linear Transformation / 1.9：
Linear Models in Business, Science, and Engineering / 1.10：
Supplementary Exercises
Matrix Algebra / 2：
Introductory Example: Computer Models in Aircraft Design
Matrix Operations / 2.1：
The Inverse of a Matrix / 2.2：
Characterizations of Invertible Matrices / 2.3：
Partitioned Matrices / 2.4：
Matrix Factorizations / 2.5：
The Leontief Input=Output Model / 2.6：
Applications to Computer Graphics / 2.7：
Subspaces of Rn / 2.8：
Dimension and Rank / 2.9：
Determinants / 3：
Introductory Example: Determinants in Analytic Geometry
Introduction to Determinants / 3.1：
Properties of Determinants / 3.2：
Cramer's Rule, Volume, and Linear Transformations / 3.3：
Vector Spaces / 4：
Introductory Example: Space Flight and Control Systems
Vector Spaces and Subspaces / 4.1：
Null Spaces, Column Spaces, and Linear Transformations / 4.2：
Linearly Independent Sets Bases / 4.3：
Coordinate Systems / 4.4：
The Dimension of a Vector Space / 4.5：
Rank / 4.6：
Change of Basis / 4.7：
Applications to Difference Equations / 4.8：
Applications to Markov Chains / 4.9：
Eigenvalues and Eigenvectors / 5：
Introductory Example: Dynamical Systems and Spotted Owls
Eigenvectors and Eigenvalues / 5.1：
The Characteristic Equation / 5.2：
Diagonalization / 5.3：
Eigenvectors and Linear Transformations / 5.4：
Complex Eigenvalues / 5.5：
Discrete Dynamical Systems / 5.6：
Applications to Differential Equations / 5.7：
Iterative Estimates for Eigenvalues / 5.8：
Orthogonality and Least Squares / 6：
Introductory Example: Readjusting the North American Datum
Inner Product, Length, and Orthogonality / 6.1：
Orthogonal Sets / 6.2：
Orthogonal Projections / 6.3：
The Gram-Schmidt Process / 6.4：
Least-Squares Problems / 6.5：
Applications to Linear Models / 6.6：
Inner Product Spaces / 6.7：
Applications of Inner Product Spaces / 6.8：
Symmetric Matrices and Quadratic Forms / Chapter 7：
Introductory Example: Multichannel Image Processing
Diagonalization of Symmetric Matrices / 7.1：
Quadratic Forms / 7.2：
Constrained Optimization / 7.3：
The Singular Value Decomposition / 7.4：
Applications to Image Processing and Statistics / 7.5：
Supplementary Exercises (ONLINE ONLY)
The Geometry of Vector Spaces / 8：
Introductory Example: The Platonic Solids
Affine Combinations / 8.1：
Affine Independence / 8.2：
Convex Combinations / 8.3：
Hyperplanes / 8.4：
Polytopes / 8.5：
Curves and Surfaces / 8.6：
Optimization / 9：
Introductory Example: The Berlin Airlift
Matrix Games / 9.1：
Linear Programming - Geometric Method / 9.2：
Linear Programming - Simplex Method / 9.3：
Duality / 9.4：
Appendices
Uniqueness of the Reduced Echelon Form / A：
Complex Numbers / B：
Glossary
Answers to Odd-Numbered Exercises
Index
Linear Equations in Linear Algebra / 1：
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations / 1.1：
6.

図書
図書
6. Differential equations & linear algebra. International ed.
C. Henry Edwards, David E. Penney
出版情報: Upper Saddle River, N.J. : Prentice Hall International, c2001  xiii, 684, 48, 6 p. ; 24 cm.
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First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
Direction Fields and Solution Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods / 2：
Population Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Linear Systems and Matrices / 3：
Introduction to Linear Systems
Matrices and Gaussian Elimination
Reduced Row-Echelon Matrices
Matrix Operations
Inverses of Matrices
Determinants
Linear Equations and Curve Fitting
Vector Spaces / 4：
The Vector Space R
The Vector Space Rn and Subspaces
Linear Combinations and Independence of Vectors
Bases and Dimension for Vector Spaces
General Vector Spaces
Linear Equations of Higher Order / 5：
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Undetermined Coefficients and Variation of Parameters
Forced Oscillations and Resonance
Eigenvalues and Eigenvectors / 6：
Introduction to Eigenvalues
Diagonalization of Matrices
Applications Involving Powers of Matrices
Linear Systems of Differential Equations / 7：
First-Order Systems and Applications
Matrices and Linear Systems
The Eigenvalue Method for Linear Systems
Second-Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Numerical Methods for Systems
Matrix Exponential Methods / 8：
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Spectral Decomposition Methods
Nonlinear Systems and Phenomena / 9：
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Laplace Transform Methods / 10：
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Forcing Functions
Power Series Methods / 11：
Introduction and Review of Power Series
Power Series Solutions
Frobenius Series Solutions
Bessel's Equation
References for Further Study
The Existence and Uniqueness of Solutions / Appendix A：
Theory of Determinants / Appendix B：
Answers to Selected Problems
Index
First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
7.

図書
図書
7. A (terse) introduction to linear algebra
Yitzhak Katznelson, Yonatan R. Katznelson
出版情報: Providence, R.I. : American Mathematical Society, c2008  x, 215 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 44
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Vector spaces
Linear operators and matrices
Duality of vector spaces
Determinants Invariant subspaces
Operators on inner-product spaces
Structure theorems
Additional topics
Appendix
Index
Vector spaces
Linear operators and matrices
Duality of vector spaces
8.

図書
図書
8. Linear programming with MATLAB
Michael C. Ferris, Olvi L. Mangasarian, Stephen J. Wright
出版情報: Philadelphia : Society for Industrial and Applied Mathematics : Mathematical Programming Society, c2007  xi, 266 p. ; 26 cm
シリーズ名: MPS-SIAM series on optimization ; 7
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9.

図書
図書
9. Linear and projective representations of symmetric groups (: hbk)
Alexander Kleshchev
出版情報: Cambridge : Cambridge University Press, c2005  xiv, 277 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 163
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Preface
Linear Representations / Part I：
Notations and generalities / 1：
Symmetric groups I / 2：
Degenerate affine Hecke algebra / 3：
First results on Hn-modules / 4：
Crystal operators / 5：
Character calculations / 6：
Integral representations and cyclotomic Hecke algebras / 7：
Functors ei? and fi? / 8：
Construction of UZ+ and irreducible modules / 9：
Identification of the crystal / 10：
Symmetric groups II / 11：
Projective Representations / Part II：
Generalities on superalgebra / 12：
Sergeev superalgebras / 13：
Affine Sergeev superalgebras / 14：
Integral representations and cyclotomic Sergeev algebras / 15：
First results on Xn-modules / 16：
Crystal operators for Xn / 17：
Character calculations for Xn / 18：
Operators ei? and fi? / 19：
Double covers / 20：
References
Index
Preface
Linear Representations / Part I：
Notations and generalities / 1：
10.

図書
図書
10. Geršgorin and his circles
Richard S. Varga
出版情報: Berlin : Springer, c2004  x, 226 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 36
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Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
Extensions of Geršgorin's Theorem via Graph Theory / 1.2：
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3：
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4：
Geršgorin-Type Eigenvalue Inclusion Theorems / 2：
Brauer's Ovals of Cassini / 2.1：
Higher-Order Lemniscates / 2.2：
Comparison of the Brauer Sets and the Brualdi Sets / 2.3：
The Sharpness of Brualdi Lemniscate Sets / 2.4：
An Example / 2.5：
More Eigenvalue Inclusion Results / 3：
The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1：
The Field of Values of a Matrix / 3.2：
Newer Eigenvalue Inclusion Sets / 3.3：
The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4：
Minimal Geršgorin Sets and Their Sharpness / 4：
Minimal Geršgorin Sets / 4.1：
Minimal Geršgorin Sets via Permutations / 4.2：
A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3：
G-Functions / 5：
The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1：
Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2：
Minimal G-Functions / 5.3：
Minimal G-Functions with Small Domains of Dependence / 5.4：
Connections with Brauer Sets and Generalized Brualdi Sets / 5.5：
Geršgorin-Type Theorems for Partitioned Matrices / 6：
Partitioned Matrices and Block Diagonal Dominance / 6.1：
A Different Norm Approach / 6.2：
A Variation on a Theme by Brualdi / 6.3：
G-Functions in the Partitioned Case / 6.4：
Geršgorin's Paper from 1931, and Comments / Appendix A：
Vector Norms and Induced Operator Norms / Appendix B：
The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C：
Matlab 6 Programs / Appendix D：
References
Preface / I：
Basic Theory / 1：
Geršgorin's Theorem / 1.1：
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