1.

David C. Lay

 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：
2.

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 所蔵情報: loading…

 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：
3.

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 所蔵情報: loading…

 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：
4.

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 所蔵情報: loading…

 Relativity before 1905 Special relativityÃ¹kinematics Special relativityÃ¹kinetics Arbitrary frames Surfaces and curvatures Intrinsic geometry General relativity Consequences
 Relativity before 1905 Special relativityÃ¹kinematics Special relativityÃ¹kinetics
5.

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 所蔵情報: loading…

 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
6.

Carl Meyer
 出版情報: Philadelphia : Society for Industrial and Applied Mathematics (SIAM), c2000  2 v. ; 25 cm. 所蔵情報: loading…

 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：
7.

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 所蔵情報: loading…

 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：
8.

Peter Deuflhard
 出版情報: Berlin ; Tokyo : Springer, c2004  xii, 424 p. ; 24 cm シリーズ名: Springer series in computational mathematics ; 35 所蔵情報: loading…

 Outline of Contents Introduction / 1： Newton-Raphson Method for Scalar Equations / 1.1：
9.

Steven Roman
 出版情報: New York : Springer, c2005  xvi, 482 p. ; 24 cm シリーズ名: Graduate texts in mathematics ; 135 所蔵情報: loading…

 Preface to the Second Edition Preface to the First Edition Preliminaries Algebraic Structures / Part 1： Basic Linear Algebra / Part I： Vector Spaces / 1： Subspaces Direct Sums Spanning Sets and Linear Independence The Dimension of a Vector Space Ordered Bases and Coordinate Matrices The Row and Column Spaces of a Matrix The Complexification of a Real Vector Space Exercises Linear Transformations / 2： Isomorphisms The Kernel and Image of a Linear Transformation Linear Transformations from F[superscript n] to F[superscript m] The Rank Plus Nullity Theorem Change of Basis Matrices The Matrix of a Linear Transformation Change of Bases for Linear Transformations Equivalence of Matrices Similarity of Matrices Similarity of Operators Invariant Subspaces and Reducing Paris Topological Vector Spaces Linear Operators on V[superscript C] The Isomorphism Theorems / 3： Quotient Spaces The Universal Property of Quotients and the First Isomorphism Theorem Quotient Spaces, Complements and Codimension Additional Isomorphism Theorems Linear Functionals Dual Bases Reflexivity Annihilators Operator Adjoints Modules I: Basic Properties / 4： Modules Motivation Submodules Spanning Sets Linear Independence Torsion Elements Free Modules Homomorphisms Quotient Modules The Correspondence and Isomorphism Theorems Direct Sums and Direct Summands Modules Are Not As Nice As Vector Spaces Modules II: Free and Noetherian Modules / 5： The Rank of a Free Module Free Modules and Epimorphisms Noetherian Modules The Hilbert Basis Theorem Modules over a Principal Ideal Domain / 6： Annihilators and Orders Cyclic Modules Free Modules over a Principal Ideal Domain Torsion-Free and Free Modules Prelude to Decomposition: Cyclic Modules The First Decomposition A Look Ahead The Primary Decomposition The Cyclic Decomposition of a Primary Module The Primary Cyclic Decomposition Theorem The Invariant Factor Decomposition The Structure of a Linear Operator / 7： A Brief Review The Module Associated with a Linear Operator Orders and the Minimal Polynomial Cyclic Submodules and Cyclic Subspaces Summary The Decomposition of V[subscript tau] The Rational Canonical Form Eigenvalues and Eigenvectors / 8： The Characteristic Polynomial of an Operator Geometric and Algebraic Multiplicities The Jordan Canonical Form Triangularizability and Schur's Lemma Diagonalizable Operators Projections The Algebra of Projections Resolutions of the Identity Spectral Resolutions Projections and Invariance Real and Complex Inner Product Spaces / 9： Norm and Distance Isometries Orthogonality Orthogonal and Orthonormal Sets The Projection Theorem and Best Approximations Orthogonal Direct Sums The Riesz Representation Theorem Structure Theory for Normal Operators / 10： The Adjoint of a Linear Operator Unitary Diagonalizability Normal Operators Special Types of Normal Operators Self-Adjoint Operators Unitary Operators and Isometries The Structure of Normal Operators Matrix Versions Orthogonal Projections Orthogonal Resolutions of the Identity The Spectral Theorem Spectral Resolutions and Functional Calculus Positive Operators The Polar Decomposition of an Operator Topics / Part II： Metric Vector Spaces: The Theory of Bilinear Forms / 11： Symmetric, Skew-Symmetric and Alternate Forms The Matrix of a Bilinear Form Quadratic Forms Orthogonal Complements and Orthogonal Direct Sums Hyperbolic Spaces Nonsingular Completions of a Subspace The Witt Theorems: A Preview The Classification Problem for Metric Vector Spaces Symplectic Geometry The Structure of Orthogonal Geometries: Orthogonal Bases The Classification of Orthogonal Geometries: Canonical Forms The Orthogonal Group The Witt's Theorems for Orthogonal Geometries Maximal Hyperbolic Subspaces of an Orthogonal Geometry Metric Spaces / 12： The Definition Open and Closed Sets Convergence in a Metric Space The Closure of a Set Dense Subsets Continuity Completeness The Completion of a Metric Space Hilbert Spaces / 13： Infinite Series An Approximation Problem Hilbert Bases Fourier Expansions A Characterization of Hilbert Bases Hilbert Dimension A Characterization of Hilbert Spaces Tensor Products / 14： Universality Bilinear Maps When Is a Tensor Product Zero? Coordinate Matrices and Rank Characterizing Vectors in a Tensor Product Defining Linear Transformations on a Tensor Product The Tensor Product of Linear Transformations Change of Base Field Multilinear Maps and Iterated Tensor Products Tensor Spaces Special Multilinear Maps Graded Algebras The Symmetric Tensor Algebra The Antisymmetric Tensor Algebra: The Exterior Product Space The Determinant Positive Solutions to Linear Systems: Convexity and Separation / 15： Convex, Closed and Compact Sets Convex Hulls Linear and Affine Hyperplanes Separation Affine Geometry / 16： Affine Combinations Affine Hulls The Lattice of Flats Affine Independence Affine Transformations Projective Geometry Operator Factorizations: QR and Singular Value / 17： The QR Decomposition Singular Values The Moore-Penrose Generalized Inverse Least Squares Approximation The Umbral Calculus / 18： Formal Power Series The Umbral Algebra Formal Power Series as Linear Operators Sheffer Sequences Examples of Sheffer Sequences Umbral Operators and Umbral Shifts Continuous Operators on the Umbral Algebra Umbral Operators and Automorphisms of the Umbral Algebra Umbral Shifts and Derivations of the Umbral Algebra The Transfer Formulas A Final Remark References Index
 Preface to the Second Edition Preface to the First Edition Preliminaries
10.

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 所蔵情報: loading…

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