实例介绍
【实例简介】
矩阵数学，Matrix Mathematics - Theory,Facts,and Formulas 2ed_Dennis S.Bernstein(Princeton 2009)，资源来自互联网
Matrix Mathematics Theory, Facts, and Formulas Dennis s. bernstein PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c2009 by Princeton University Press Published by Princeton University Press 41 William Street. Princeton. New Jersey 08540 In the United Kingdom: Princeton University Press 6 Oxford Street. Woodstock. Oxfordshire. 0X20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Bernstein, Dennis S. 1954 Matrix mathematics: theory, facts, and formulas/Dennis S. Bernstein.-2nd ed Includes bibliographical references and index ISBN 978-0-691-14039-1(pbk: alk. papery er ISBn 978-0-691-13287-7(hardcover alk. pal 1. Matrices. 2. Linear systems. I. Title (A188.H4752008 512.9434dc22 200803625 British Library Cataloging-in-Publication Data is available This book has been composed in Computer Modern and Helvetica The publisher would like to acknowledge the author of this volumc for providing tho camera-ready copy from which this book was printed Printed on acid-free paper. oo www.press.princeton.edu Printed in the United States of America 10987654321 To the memory of my parents vessels, unable to contain the great light flowing into them, shatter and break. .. the remains of the broken vessels fall,. into the lowest world. where they remain scattered and hidden D.W. Menzi and Z. Padeh The Tree of life, Chayyim vital's Introduction to the kabbalah Isaac luria. ason aaronson Northvale. 1999 Thor... placed the horn to his lips... He drank with all his might and kept drinking as long as ever he was able; when he paused to look, he could see that the level had sunk a little.. for the other end lay out in the ocean itself P.A. Munch, Norse Mythology AMS P York. 1970 Contents Preface to the Second Edition Preface to the first Edition Special Symbols XXI Conventions, Notation, and Terminology XXXIII 1. Preliminaries Logic and sets 1.2 Funct 1.3 Relations 1.4 Gra 8 1.5 Facts on Logic, Sets, Functions, and Relations 10 6 Facts on graph 13 Facts on Binomial Identities and Sums 14 1.8 Facts on Convex Functions 21 1. 9 Facts on Scalar Identities and Inequalities in One Variable 22 1.10 Facts on Scalar identities and Inequalities in Two variable 30 1.11 Facts on Scalar Identities and Inequalities in Three Variables 39 1.12 Facts on Scalar Identities and Inequalities in Four Variables 46 1.13 Facts on Scalar Identities and Inequalities in Six Variables 47 1.14 Facts on Scalar Identities and Inequalities in Eight Variables 47 1.15 Facts on Scalar Identities and Inequalities in n variable 48 1.16 Facts on scalar identities and inequalities in 2n variable 60 1.17 Facts on Scalar Identities and Inequalities in 3n Variables 67 1.18 Facts on Scalar Identities and Inequalities in Complex Variables 68 1.19 Facts on Trigonometric and Hyperbolic Identities 74 1.20Notes 76 2. Basic Matrix Properties 77 Matrix Algebra 77 2 Transpose and Inner Product 84 2.3 Convex Sets, Cones, and Subspaces 2. 4 Range and Null Spacel 93 2.5 Rank and Defect 95 2.6 Invertibility 98 CONTENTS 7 The Determinant 102 8 Partitioned matrices 106 2.9 Facts on Polars Cones. Dual cones, Convex hulls, and sub spaces 110 10 Facts on Range, Null Space, Rank, and Defect 115 2.11 Facts on the Range Rank, Null Space, and Defect of Partitioned matrices 120 2.12 Facts on the Inner Product, Outer Product, Trace, and matrix Powers 126 13 Facts on the Determinant 128 12 14 Facts on the Determinant of Partitioned Matrices 132 2.15 Facts on Left and Right Inverses 140 2.16 Facts on the Adjugate and Inverses 141 2.17 Facts on the Inverse of Partitioned Matrices 146 2.18 Facts on Commutators 149 2.19 Facts on Complex Matrices 151 2.20 Facts on Geometry 154 2.21 Facts on Mai 162 12.22 Notes 164 3. Matrix Classes and Transformations 165 Matrix Class 165 3.2 Matrices Bas Graphs 170 3.3 Lie Algebras and Groups 171 34 Matrix Transformations 173 3.5 Projectors. Idempotent Matrices, and Subspaces 175 6 Facts on Group-Invertible and Range-Hermitian matrices 177 Facts on Normal, Hermitian, and Skew-Hermitian Matrices 178 3.8 Facts on Commutators 184 3.9 Facts on Linear Interpolation 185 3.10 Facts on the Cross Product 186 3. 11 Facts on Unitary and Shifted-Unitary Matrices 189 3.12 Facts on Idempotent Matrices 198 3.13 Facts on Projectors 206 13.14 Facts on Reflectors 3.15 Facts on Involutory Matrices 5)1 3.16 Facts on Tripotent Matrices 212 3. 17 Facts on Nilpotent Matrices 3.18 Facts on Hankel and Toeplitz Matrice 215 13.19 Facts on Hamiltonian and Symplectic Matrices 216 3.20 Facts on Miscellaneous Types of Matrices 217 3.21 Facts on groups 221 Facts on Quaternions 225 3.23 Note 4. Polynomial Matrices and Rational Transfer Functions 231 4.1 Polynomials 4.2 Polynomial Matrices 234 4.3 The Smith Decomposition and similarity Invariants 2:36 【实例截图】
【核心代码】
矩阵数学，Matrix Mathematics - Theory,Facts,and Formulas 2ed_Dennis S.Bernstein(Princeton 2009)，资源来自互联网
Matrix Mathematics Theory, Facts, and Formulas Dennis s. bernstein PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c2009 by Princeton University Press Published by Princeton University Press 41 William Street. Princeton. New Jersey 08540 In the United Kingdom: Princeton University Press 6 Oxford Street. Woodstock. Oxfordshire. 0X20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Bernstein, Dennis S. 1954 Matrix mathematics: theory, facts, and formulas/Dennis S. Bernstein.-2nd ed Includes bibliographical references and index ISBN 978-0-691-14039-1(pbk: alk. papery er ISBn 978-0-691-13287-7(hardcover alk. pal 1. Matrices. 2. Linear systems. I. Title (A188.H4752008 512.9434dc22 200803625 British Library Cataloging-in-Publication Data is available This book has been composed in Computer Modern and Helvetica The publisher would like to acknowledge the author of this volumc for providing tho camera-ready copy from which this book was printed Printed on acid-free paper. oo www.press.princeton.edu Printed in the United States of America 10987654321 To the memory of my parents vessels, unable to contain the great light flowing into them, shatter and break. .. the remains of the broken vessels fall,. into the lowest world. where they remain scattered and hidden D.W. Menzi and Z. Padeh The Tree of life, Chayyim vital's Introduction to the kabbalah Isaac luria. ason aaronson Northvale. 1999 Thor... placed the horn to his lips... He drank with all his might and kept drinking as long as ever he was able; when he paused to look, he could see that the level had sunk a little.. for the other end lay out in the ocean itself P.A. Munch, Norse Mythology AMS P York. 1970 Contents Preface to the Second Edition Preface to the first Edition Special Symbols XXI Conventions, Notation, and Terminology XXXIII 1. Preliminaries Logic and sets 1.2 Funct 1.3 Relations 1.4 Gra 8 1.5 Facts on Logic, Sets, Functions, and Relations 10 6 Facts on graph 13 Facts on Binomial Identities and Sums 14 1.8 Facts on Convex Functions 21 1. 9 Facts on Scalar Identities and Inequalities in One Variable 22 1.10 Facts on Scalar identities and Inequalities in Two variable 30 1.11 Facts on Scalar Identities and Inequalities in Three Variables 39 1.12 Facts on Scalar Identities and Inequalities in Four Variables 46 1.13 Facts on Scalar Identities and Inequalities in Six Variables 47 1.14 Facts on Scalar Identities and Inequalities in Eight Variables 47 1.15 Facts on Scalar Identities and Inequalities in n variable 48 1.16 Facts on scalar identities and inequalities in 2n variable 60 1.17 Facts on Scalar Identities and Inequalities in 3n Variables 67 1.18 Facts on Scalar Identities and Inequalities in Complex Variables 68 1.19 Facts on Trigonometric and Hyperbolic Identities 74 1.20Notes 76 2. Basic Matrix Properties 77 Matrix Algebra 77 2 Transpose and Inner Product 84 2.3 Convex Sets, Cones, and Subspaces 2. 4 Range and Null Spacel 93 2.5 Rank and Defect 95 2.6 Invertibility 98 CONTENTS 7 The Determinant 102 8 Partitioned matrices 106 2.9 Facts on Polars Cones. Dual cones, Convex hulls, and sub spaces 110 10 Facts on Range, Null Space, Rank, and Defect 115 2.11 Facts on the Range Rank, Null Space, and Defect of Partitioned matrices 120 2.12 Facts on the Inner Product, Outer Product, Trace, and matrix Powers 126 13 Facts on the Determinant 128 12 14 Facts on the Determinant of Partitioned Matrices 132 2.15 Facts on Left and Right Inverses 140 2.16 Facts on the Adjugate and Inverses 141 2.17 Facts on the Inverse of Partitioned Matrices 146 2.18 Facts on Commutators 149 2.19 Facts on Complex Matrices 151 2.20 Facts on Geometry 154 2.21 Facts on Mai 162 12.22 Notes 164 3. Matrix Classes and Transformations 165 Matrix Class 165 3.2 Matrices Bas Graphs 170 3.3 Lie Algebras and Groups 171 34 Matrix Transformations 173 3.5 Projectors. Idempotent Matrices, and Subspaces 175 6 Facts on Group-Invertible and Range-Hermitian matrices 177 Facts on Normal, Hermitian, and Skew-Hermitian Matrices 178 3.8 Facts on Commutators 184 3.9 Facts on Linear Interpolation 185 3.10 Facts on the Cross Product 186 3. 11 Facts on Unitary and Shifted-Unitary Matrices 189 3.12 Facts on Idempotent Matrices 198 3.13 Facts on Projectors 206 13.14 Facts on Reflectors 3.15 Facts on Involutory Matrices 5)1 3.16 Facts on Tripotent Matrices 212 3. 17 Facts on Nilpotent Matrices 3.18 Facts on Hankel and Toeplitz Matrice 215 13.19 Facts on Hamiltonian and Symplectic Matrices 216 3.20 Facts on Miscellaneous Types of Matrices 217 3.21 Facts on groups 221 Facts on Quaternions 225 3.23 Note 4. Polynomial Matrices and Rational Transfer Functions 231 4.1 Polynomials 4.2 Polynomial Matrices 234 4.3 The Smith Decomposition and similarity Invariants 2:36 【实例截图】
【核心代码】
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