Verfügbarkeit: Matrix analysis and applied linear algebra

Matrix analysis and applied linear algebra: [1] [Hauptband]

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Bibliographische Detailangaben
Beteilige Person:	Meyer, Carl D. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Philadelphia SIAM [2000]
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009081415&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xii, 718 Seiten Illustrationen, Diagramme CD-ROM (12 cm)
ISBN:	0898714540

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface............................................... ix 1. Linear Equations.........................................1 1.1 Introduction.......................................1 1.2 Gaussian Elimination and Matrices..................3 1.3 Gauss-Jordan Method...............................15 1.4 Two-Point Boundary Value Problems.................18 1.5 Making Gaussian Elimination Work..................21 1.6 Ill-Conditioned Systems...........................33 2. Rectangular Systems and Echelon Forms ... 41 2.1 Row Echelon Form and Rank.........................41 2.2 Reduced Row Echelon Form..........................47 2.3 Consistency of Linear Systems.....................53 2.4 Homogeneous Systems...............................57 2.5 Nonhomogeneous Systems............................64 2.6 Electrical Circuits...............................73 3. Matrix Algebra..........................................79 3.1 From Ancient China to Arthur Cayley...............79 3.2 Addition and Transposition .......................81 3.3 Linearity.........................................89 3.4 Why Do It This Way................................93 3.5 Matrix Multiplication.............................95 3.6 Properties of Matrix Multiplication..............105 3.T Matrix Inversion.................................115 3.8 Inverses of Sums and Sensitivity.................124 3.9 Elementary Matrices and Equivalence..............131 3.10 The LU Factorization.............................141 4. Vector Spaces..........................................159 4.1 Spaces and Subspaces.............................159 4.2 Four Fundamental Subspaces..................... 169 4.3 Linear Independence............................ 181 4.4 Basis and Dimension............................ 194 Contents 4.5 More about Rank................................ 4.6 Classical Least Squares........................22 * 4.7 Linear Transformations.........................2·^ 4.8 Change of Basis and Similarity................. 4.9 Invariant Subspaces............................ 2 r’9 5. Norms, Inner Products, and Orthogonality . . 269 5.1 Vector Norms...................................2()ii 5.2 Matrix Norms...................................2?9 5.3 Inner-Product Spaces........................... 5.4 Orthogonal Vectors............................. 5.5 Gram-Schmidt Procedure.........................307 5.6 Unitary and Orthogonal Matrices...................120 5.7 Orthogonal Reduction...........................341 5.8 Discrete Fourier Transform.....................356 5.9 Complementary Subspaces........................383 5.10 Range-Nullspace Decomposition.....................394 5.11 Orthogonal Decomposition..........................403 5.12 Singular Value Decomposition......................411 5.13 Orthogonal Projection.............................429 5.14 Why Least Squares?................................446 5.15 Angles between Subspaces.......................450 6. Determinants.........................................459 6.1 Determinants......................................459 6.2 Additional Properties of Determinants..........475 7. Eigenvalues and Eigenvectors.........................489 7.1 Elementary Properties of Eigensystems.............489 7.2 Diagonalization by Similarity Transformations . . 505 7.3 Functions of Diagonalizable Matrices..............525 7.4 Systems of Differential Equations..............541 7.5 Normal Matrices..................................... 7.6 Positive Definite Matrices........................558 7.7 Nilpotent Matrices and Jordan Structure .... 574 7.8 Jordan Form......................................... 7.9 Functions of Nondiagonalizable Matrices...........599 Contents Vll 7.10 Difference Equations, Limits, and Summability . . 616 7.11 Minimum Polynomials and Krylov Methods ... 642 8. Perron-Frobenius Theory............................661 8.1 Introduction..................................661 8.2 Positive Matrices.............................663 8.3 Nonnegative Matrices..........................670 8.4 Stochastic Matrices and Markov Chains.........687 Index..............................................705
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spellingShingle	Meyer, Carl D. Matrix analysis and applied linear algebra
title	Matrix analysis and applied linear algebra
title_auth	Matrix analysis and applied linear algebra
title_exact_search	Matrix analysis and applied linear algebra
title_full	Matrix analysis and applied linear algebra [1] [Hauptband] Carl Meyer, North Carolina State University, Raleigh, NC
title_fullStr	Matrix analysis and applied linear algebra [1] [Hauptband] Carl Meyer, North Carolina State University, Raleigh, NC
title_full_unstemmed	Matrix analysis and applied linear algebra [1] [Hauptband] Carl Meyer, North Carolina State University, Raleigh, NC
title_short	Matrix analysis and applied linear algebra
title_sort	matrix analysis and applied linear algebra hauptband
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