CiNii Books - Linear algebra

For courses in Advanced Linear Algebra. Illustrates the power of linear algebra through practical applications This acclaimed theorem-proof text presents a careful treatment of the principal topics of linear algebra. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Applications to such areas as differential equations, economics, geometry, and physics appear throughout, and can be included at the instructor's discretion. 0134860241 / 9780134860244 Linear Algebra, 5/e

Table of Contents

Table of Contents * Sections denoted by an asterisk are optional. Vector Spaces 1.1 Introduction 1.2 Vector Spaces 1.3 Subspaces 1.4 Linear Combinations and Systems of Linear Equations 1.5 Linear Dependence and Linear Independence 1.6 Bases and Dimension 1.7* Maximal Linearly Independent Subsets Index of Definitions Linear Transformations and Matrices 2.1 Linear Transformations, Null Spaces, and Ranges 2.2 The Matrix Representation of a Linear Transformation 2.3 Composition of Linear Transformations and Matrix Multiplication 2.4 Invertibility and Isomorphisms 2.5 The Change of Coordinate Matrix 2.6* Dual Spaces 2.7* Homogeneous Linear Differential Equations with Constant Coefficients Index of Definitions Elementary Matrix Operations and Systems of Linear Equations 3.1 Elementary Matrix Operations and Elementary Matrices 3.2 The Rank of a Matrix and Matrix Inverses 3.3 Systems of Linear Equations - Theoretical Aspects 3.4 Systems of Linear Equations - Computational Aspects Index of Definitions Determinants 4.1 Determinants of Order 2 4.2 Determinants of Order n 4.3 Properties of Determinants 4.4 Summary|Important Facts about Determinants 4.5* A Characterization of the Determinant Index of Definitions Diagonalization 5.1 Eigenvalues and Eigenvectors 5.2 Diagonalizability 5.3* Matrix Limits and Markov Chains 5.4 Invariant Subspaces and the Cayley-Hamilton Theorem Index of Definitions Inner Product Spaces 6.1 Inner Products and Norms 6.2 The Gram-Schmidt Orthogonalization Process and Orthogonal Complements 6.3 The Adjoint of a Linear Operator 6.4 Normal and Self-Adjoint Operators 6.5 Unitary and Orthogonal Operators and Their Matrices 6.6 Orthogonal Projections and the Spectral Theorem 6.7* The Singular Value Decomposition and the Pseudoinverse 6.8* Bilinear and Quadratic Forms 6.9* Einstein's Special Theory of Relativity 6.10* Conditioning and the Rayleigh Quotient 6.11* The Geometry of Orthogonal Operators Index of Definitions Canonical Forms 7.1 The Jordan Canonical Form I 7.2 The Jordan Canonical Form II 7.3 The Minimal Polynomial 7.4* The Rational Canonical Form Index of Definitions Appendices Sets Functions Fields Complex Numbers Polynomials Answers to Selected Exercises Index

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Linear algebra

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