Format:
1 Online-Ressource (xxxix, 1139 pages)
Edition:
2nd ed
Edition:
Online-Ausg.
ISBN:
0691132879
,
0691140391
,
1400833345
,
9780691132877
,
9780691140391
,
9781400833344
,
1283256010
Content:
Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identitites, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks
Content:
Preliminaries -- Basic matrix properties -- Matrix classes and transformations -- Polynomial matrices and rational transfer functions -- Matrix decompositions -- Generalized inverses -- Kronecker and Schur algebra -- Positive-semidefinite matrices -- Norms -- Functions of matrices and their derivatives -- The matrix exponential and stability theory -- Linear systems and control theory
Note:
Includes bibliographical references and indexes
,
Cover; Contents; Preface to the Second Edition; Preface to the First Edition; Special Symbols; Conventions, Notation, and Terminology; Chapter One: Preliminaries; 1.1 Logic; 1.2 Sets; 1.3 Integers, Real Numbers, and Complex Numbers; 1.4 Functions; 1.5 Relations; 1.6 Graphs; 1.7 Facts on Logic, Sets, Functions, and Relations; 1.8 Facts on Graphs; 1.9 Facts on Binomial Identities and Sums; 1.10 Facts on Convex Functions; 1.11 Facts on Scalar Identities and Inequalities in One Variable; 1.12 Facts on Scalar Identities and Inequalities in Two Variables
,
1.13 Facts on Scalar Identities and Inequalities in Three Variables1.14 Facts on Scalar Identities and Inequalities in Four Variables; 1.15 Facts on Scalar Identities and Inequalities in Six Variables; 1.16 Facts on Scalar Identities and Inequalities in Eight Variables; 1.17 Facts on Scalar Identities and Inequalities in n Variables; 1.18 Facts on Scalar Identities and Inequalities in 2n Variables; 1.19 Facts on Scalar Identities and Inequalities in 3n Variables; 1.20 Facts on Scalar Identities and Inequalities in Complex Variables; 1.21 Facts on Trigonometric and Hyperbolic Identities
,
1.22 NotesChapter Two: Basic Matrix Properties; 2.1 Matrix Algebra; 2.2 Transpose and Inner Product; 2.3 Convex Sets, Cones, and Subspaces; 2.4 Range and Null Space; 2.5 Rank and Defect; 2.6 Invertibility; 2.7 The Determinant; 2.8 Partitioned Matrices; 2.9 Facts on Polars, Cones, Dual Cones, Convex Hulls, and Subspaces; 2.10 Facts on Range, Null Space, Rank, and Defect; 2.11 Facts on the Range, Rank, Null Space, and Defect of Partitioned Matrices; 2.12 Facts on the Inner Product, Outer Product, Trace, and Matrix Powers; 2.13 Facts on the Determinant
,
2.14 Facts on the Determinant of Partitioned Matrices2.15 Facts on Left and Right Inverses; 2.16 Facts on the Adjugate and Inverses; 2.17 Facts on the Inverse of Partitioned Matrices; 2.18 Facts on Commutators; 2.19 Facts on Complex Matrices; 2.20 Facts on Geometry; 2.21 Facts on Majorization; 2.22 Notes; Chapter Three: Matrix Classes and Transformations; 3.1 Matrix Classes; 3.2 Matrices Related to Graphs; 3.3 Lie Algebras and Groups; 3.4 Matrix Transformations; 3.5 Projectors, Idempotent Matrices, and Subspaces; 3.6 Facts on Group-Invertible and Range-Hermitian Matrices
,
3.7 Facts on Normal, Hermitian, and Skew-Hermitian Matrices3.8 Facts on Commutators; 3.9 Facts on Linear Interpolation; 3.10 Facts on the Cross Product; 3.11 Facts on Unitary and Shifted-Unitary Matrices; 3.12 Facts on Idempotent Matrices; 3.13 Facts on Projectors; 3.14 Facts on Reflectors; 3.15 Facts on Involutory Matrices; 3.16 Facts on Tripotent Matrices; 3.17 Facts on Nilpotent Matrices; 3.18 Facts on Hankel and Toeplitz Matrices; 3.19 Facts on Tridiagonal Matrices; 3.20 Facts on Hamiltonian and Symplectic Matrices; 3.21 Facts on Matrices Related to Graphs
,
3.22 Facts on Triangular, Irreducible, Cauchy, Dissipative, Contractive, and Centrosymmetric Matrices
,
In English
Additional Edition:
ISBN 9780691132877
Additional Edition:
Erscheint auch als Druck-Ausgabe Bernstein, Dennis S., 1954- Matrix mathematics Princeton, N.J : Princeton University Press, ©2009
Additional Edition:
Erscheint auch als Druck-Ausgabe Bernstein, Dennis S., 1954 - Matrix mathematics Princeton, NJ [u.a.] : Princeton University Press, 2009 ISBN 9780691140391
Additional Edition:
ISBN 9780691132877
Additional Edition:
ISBN 0691140391
Additional Edition:
ISBN 0691132879
Language:
English
Subjects:
Mathematics
Keywords:
Matrizentheorie
;
Matrix
;
Determinante
;
Matrizenpolynom
;
Lineares System
;
Lineare Kontrolltheorie
;
Electronic books
;
Lehrbuch
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
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