Matrix methods : applied linear algebra /

Matrix Methods: Applied Linear Algebra, 3e, as a textbook, provides a unique and comprehensive balance between the theory and computation of matrices. The application of matrices is not just for mathematicians. The use of matrices in other disciplines has grown dramatically over the years in respons...

Szczegółowa specyfikacja

Opis bibliograficzny
1. autor: Bronson, Richard
Korporacja: Anne and Joseph Trachtman Memorial Book Fund
Kolejni autorzy: Costa, Gabriel B.
Format: Książka
Język:English
Wydane: Amsterdam ; Boston : EAcademic Press, [2009]
Wydanie:Third edition.
Hasła przedmiotowe:
Spis treści:
  • 1 Matrices 1
  • 1.2 Operations 6
  • 1.3 Matrix Multiplication 9
  • 1.4 Special Matrices 19
  • 1.5 Submatrices and Partitioning 29
  • 1.6 Vectors 33
  • 1.7 The Geometry of Vectors 37
  • 2 Simultaneous Linear Equations 43
  • 2.1 Linear Systems 43
  • 2.2 Solutions by Substitution 50
  • 2.3 Gaussian Elimination 54
  • 2.4 Pivoting Strategies 65
  • 2.5 Linear Independence 71
  • 2.6 Rank 78
  • 2.7 Theory of Solutions 84
  • 3 The Inverse 93
  • 3.2 Calculating Inverses 101
  • 3.3 Simultaneous Equations 109
  • 3.4 Properties of the Inverse 112
  • 3.5 LU Decomposition 115
  • 4 An Introduction to Optimization 127
  • 4.1 Graphing Inequalities 127
  • 4.2 Modeling with Inequalities 131
  • 4.3 Solving Problems Using Linear Programming 135
  • 4.4 An Introduction to The Simplex Method 140
  • 5 Determinants 149
  • 5.2 Expansion by Cofactors 152
  • 5.3 Properties of Determinants 157
  • 5.4 Pivotal Condensation 163
  • 5.5 Inversion 167
  • 5.6 Cramer's Rule 170
  • 6 Eigenvalues and Eigenvectors 177
  • 6.2 Eigenvalues 180
  • 6.3 Eigenvectors 184
  • 6.4 Properties of Eigenvalues and Eigenvectors 190
  • 6.5 Linearly Independent Eigenvectors 194
  • 6.6 Power Methods 201
  • 7 Matrix Calculus 213
  • 7.1 Well-Defined Functions 213
  • 7.2 Cayley-Hamilton Theorem 219
  • 7.3 Polynomials of Matrices-Distinct Eigenvalues 222
  • 7.4 Polynomials of Matrices-General Case 228
  • 7.5 Functions of a Matrix 233
  • 7.6 The Function e[superscript At] 238
  • 7.7 Complex Eigenvalues 241
  • 7.8 Properties of e[superscript A] 245
  • 7.9 Derivatives of a Matrix 248
  • 8 Linear Differential Equations 257
  • 8.1 Fundamental Form 257
  • 8.2 Reduction of an nth Order Equation 263
  • 8.3 Reduction of a System 269
  • 8.4 Solutions of Systems with Constant Coefficients 275
  • 8.5 Solutions of Systems-General Case 286
  • 9 Probability and Markov Chains 297
  • 9.1 Probability: An Informal Approach 297
  • 9.2 Some Laws of Probability 301
  • 9.3 Bernoulli Trials and Combinatorics 305
  • 9.4 Modeling with Markov Chains: An Introduction 310
  • 10 Real Inner Products and Least-Square 315
  • 10.2 Orthonormal Vectors 320
  • 10.3 Projections and QR-Decompositions 327
  • 10.4 The QR-Algorithm 339
  • 10.5 Least-Squares 344
  • Appendix A Word on Technology 355.