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Scalar, Vector, and Matrix Mathematics

Scalar, Vector, and Matrix Mathematics

Autorzy
Wydawnictwo Princeton University Press
Data wydania 27/02/2018
Wydanie Pierwsze
Liczba stron 1600
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9780691176536
Kategorie Matematyka, Algebra
413.00 PLN (z VAT)
$112.68 / €97.41 / £85.68 /
Produkt dostępny
Przesyłka w 14 dni
Ilość
Do schowka

Opis książki

The essential reference book on matrices--now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. * Fully updated and expanded with new material on scalar and vector mathematics* Covers the latest results in matrix theory* Provides a list of symbols and a summary of conventions for easy and precise use* Includes an extensive bibliography with back-referencing plus an author index Praise for the previous editions: "When a matrix question is thrown my way, I will now refer my correspondents ... to Bernstein's handbook."--Philip J. Davis, SIAM News Praise for the previous editions: "The amount of material that is covered is quite impressive and well structured... I highly recommend the book as a source for retrieving or verifying matrix results that one would otherwise have to search for in the extensive literature on matrix theory."--Paul Van Dooren, IEEE Control Systems Magazine Praise for the previous editions: "The author was very successful in collecting the enormous amount of results in matrix theory in a single source... A beautiful work and an admirable performance!"--Monatshefte fur Mathematik Praise for the previous editions: "A remarkable source of m

Scalar, Vector, and Matrix Mathematics

Spis treści

Preface to the Revised and Expanded Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi

Special Symbols xxv

Conventions, Notation, and Terminology xxxvii

1. Sets, Logic, Numbers, Relations, Orderings, Graphs, and Functions 1

1.1 Sets 1

1.2 Logic 2

1.3 Relations and Orderings 5

1.4 Directed and Symmetric Graphs 9

1.5 Numbers 12

1.6 Functions and Their Inverses 16

1.7 Facts on Logic 21

1.8 Facts on Sets 22

1.9 Facts on Graphs 25

1.10 Facts on Functions 26

1.11 Facts on Integers 28

1.12 Facts on Finite Sums 36

1.13 Facts on Factorials 49

1.14 Facts on Finite Products 52

1.15 Facts on Numbers 52

1.16 Facts on Binomial Coefficients 54

1.17 Facts on Fibonacci, Lucas, and Pell Numbers 95

1.18 Facts on Arrangement, Derangement, and Catalan Numbers 103

1.19 Facts on Cycle, Subset, Eulerian, Bell, and Ordered Bell Numbers 105

1.20 Facts on Partition Numbers, the Totient Function, and Divisor Sums 113

1.21 Facts on Convex Functions 116

1.22 Notes 118

2. Equalities and Inequalities 119

2.1 Facts on Equalities and Inequalities in One Variable 119

2.2 Facts on Equalities and Inequalities in Two Variables 129

2.3 Facts on Equalities and Inequalities in Three Variables 146

2.4 Facts on Equalities and Inequalities in Four Variables 177

2.5 Facts on Equalities and Inequalities in Five Variables 183

2.6 Facts on Equalities and Inequalities in Six Variables 184

2.7 Facts on Equalities and Inequalities in Seven Variables 186

2.8 Facts on Equalities and Inequalities in Eight Variables 187

2.9 Facts on Equalities and Inequalities in Nine Variables 187

2.10 Facts on Equalities and Inequalities in Sixteen Variables 187

2.11 Facts on Equalities and Inequalities in n Variables 188

2.12 Facts on Equalities and Inequalities in 2n Variables 215

2.13 Facts on Equalities and Inequalities in 3n Variables 226

2.14 Facts on Equalities and Inequalities in 4n Variables 226

2.15 Facts on Equalities and Inequalities for the Logarithm Function 226

2.16 Facts on Equalities for Trigonometric Functions 231

2.17 Facts on Inequalities for Trigonometric Functions 246

2.18 Facts on Equalities and Inequalities for Inverse Trigonometric Functions 254

2.19 Facts on Equalities and Inequalities for Hyperbolic Functions 261

2.20 Facts on Equalities and Inequalities for Inverse Hyperbolic Functions 264

2.21 Facts on Equalities and Inequalities in Complex Variables 266

2.22 Notes 276

3. Basic Matrix Properties 277

3.1 Vectors 277

3.2 Matrices 280

3.3 Transpose and Inner Product 285

3.4

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