Matrix mathematics: theory, facts, and formulas
Gespeichert in:
| Späterer Titel: | Scalar, vector, and matrix mathematics |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2009
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XXXIX, 1139 S. graph. Darst. |
| ISBN: | 9780691140391 9780691132877 |
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Datensatz im Suchindex
| _version_ | 1804140696687345664 |
|---|---|
| adam_text | MATRIX MATHEMATICS THEORY, FACTS, AND FORMULAS DENNIS S. BERNSTEIN
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD CONTENTS PREFACE TO THE
SECOND EDITION XV PREFACE TO THE FIRST EDITION XVII SPECIAL SYMBOLS XXI
CONVENTIONS, NOTATION, AND TERMINOLOGY XXXIII 1. PRELIMINARIES 1 1.1
LOGIC 1 1.2 SETS 2 1.3 INTEGERS, REAL NUMBERS, AND COMPLEX NUMBERS 3 1.4
FUNCTIONS 4 1.5 RELATIONS 6 1.6 GRAPHS 9 1.7 FACTS ON LOGIC, SETS,
FUNCTIONS, AND RELATIONS 11 1.8 FACTS ON GRAPHS 15 1.9 FACTS ON BINOMIAL
IDENTITIES AND SUMS 16 1.10 FACTS ON CONVEX FUNCTIONS 23 1.11 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN ONE VARIABLE 25 1.12 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN TWO VARIABLES 33 1.13 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN THREE VARIABLES 42 1.14 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN FOUR VARIABLES 50 1.15 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN SIX VARIABLES 52 1.16 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN EIGHT VARIABLES 52 1.17 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN N VARIABLE S 52 1.18 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN 2N VARIABLES 66 1.19 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN 3N VARIABLES 74 1.20 FACTS ON
SCALAR IDENTITIES AND INEQUALITIES IN COMPLEX VARIABLES 74 1.21 FACTS ON
TRIGONOMETRIC AND HYPERBOLIC IDENTITIES 81 1.22 NOTES 84 2. BASIC MATRIX
PROPERTIES 85 2.1 MATRIX ALGEBRA 85 2.2 TRANSPOSE AND INNER PRODUCT 92
2.3 CONVEX SETS, CONES, AND SUBSPACES 97 2.4 RANGE AND NULL SPACE 101 X
CONTENTS 2.5 RANK AND DEFECT 104 2.6 INVERTIBILITY 106 2.7 THE
DETERMINANT 111 2.8 PARTITIONED MATRICES 115 2.9 FACTS ON POLARS, CONES,
DUAL CONES, CONVEX HULLS, AND SUBSPACES 119 2.10 FACTS ON RANGE, NULL
SPACE, RANK, AND DEFECT 124 2.11 FACTS ON THE RANGE, RANK, NULL SPACE,
AND DEFECT OF PARTITIONED MATRICES 130 2.12 FACTS ON THE INNER PRODUCT,
OUTER PRODUCT, TRACE, AND MATRIX POWERS 136 2.13 FACTS ON THE
DETERMINANT 139 2.14 FACTS ON THE DETERMINANT OF PARTITIONED MATRICES
144 2.15 FACTS ON LEFT AND RIGHT INVERSES 152 2.16 FACTS ON THE ADJUGATE
AND INVERSES 153 2.17 FACTS ON THE INVERSE OF PARTITIONED MATRICES 159
2.18 FACTS ON COMMUTATORS 161 2.19 FACTS ON COMPLEX MATRICES 164 2.20
FACTS ON GEOMETRY 167 2.21 FACTS ON MAJORIZATION 175 2.22 NOTES 178 3.
MATRIX CLASSES AND TRANSFORMATIONS 179 3.1 MATRIX CLASSES 179 3.2
MATRICES RELATED TO GRAPHS 184 3.3 LIE ALGEBRAS AND GROUPS 185 3.4
MATRIX TRANSFORMATIONS 188 3.5 PROJECTORS, IDEMPOTENT MATRICES, AND
SUBSPACES 190 3.6 FACTS ON GROUP-LNVERTIBLE AND RANGE-HERMITIAN MATRICES
191 3.7 FACTS ON NORMAL, HERMITIAN, AND SKEW-HERMITIAN MATRICES 192 3.8
FACTS ON COMMUTATORS 199 3.9 FACTS ON LINEAR INTERPOLATION 200 3.10
FACTS ON THE CROSS PRODUCT 202 3.11 FACTS ON UNITARY AND SHIFTED-UNITARY
MATRICES 205 3.12 FACTS ON IDEMPOTENT MATRICES 215 3.13 FACTS ON
PROJECTORS 223 3.14 FACTS ON REFLECTORS 229 3.15 FACTS ON I NVOLUTORY
MATRICES 230 3.16 FACTS ON TRIPOTENT MATRICES 231 3.17 FACTS ON
NILPOTENT MATRICES 232 3.18 FACTS ON HANKEL AND TOEPLITZ MATRICES 234
3.19 FACTS ON TRIDIAGONAL MATRICES 237 3.20 FACTS ON HAMILTONIAN AND
SYMPLECTIC MATRICES 238 3.21 FACTS ON MATRICES RELATED TO GRAPHS 240
3.22 FACTS ON TRIANGULAR, IRREDUCIBLE, CAUCHY, DISSIPATIVE, CONTRACTIVE,
AND CENTROSYMMETRIC MATRICES 240 3.23 FACTS ON GROUPS 242 3.24 FACTS ON
QUATERNIONS 247 3.25 NOTES 252 CONTENTS XI 4. POLYNOMIAL MATRICES AND
RATIONAL TRANSFER FUNCTIONS 253 4.1 POLYNOMIALS 253 4.2 POLYNOMIAL
MATRICES 256 4.3 THE SMITH DECOMPOSITION AND SIMILARITY INVARIANTS 258
4.4 EIGENVALUES 261 4.5 EIGENVECTORS 267 4.6 THE MINIMAL POLYNOMIAL 269
4.7 RATIONAL TRANSFER FUNCTIONS AND THE SMITH-MCMILLAN DECOMPOSITION 271
4.8 FACTS ON POLYNOMIALS AND RATIONAL FUNCTIONS 276 4.9 FACTS ON THE
CHARACTERISTIC AND MINIMAL POLYNOMIALS 282 4.10 FACTS ON THE SPECTRUM
288 4.11 FACTS ON GRAPHS AND NONNEGATIVE MATRICES 297 4.12 NOTES 307 5.
MATRIX DECOMPOSITIONS 309 5.1 SMITH FORM 309 5.2 MULTICOMPANION FORM 309
5.3 HYPERCOMPANION FORM AND JORDAN FORM 314 5.4 SCHUR DECOMPOSITION 318
5.5 EIGENSTRUCTURE PROPERTIES 321 5.6 SINGULAR VALUE DECOMPOSITION 328
5.7 PENCILS AND THE KRONECKER CANONICAL FORM 330 5.8 FACTS ON THE
INERTIA 334 5.9 FACTS ON MATRIX TRANSFORMATIONS FOR ONE MATRIX 338 5.10
FACTS ON MATRIX TRANSFORMATIONS FOR TWO OR MORE MATRICES 345 5.11 FACTS
ON EIGENVALUES AND SINGULAR VALUES FOR ONE MATRIX 350 5.12 FACTS ON
EIGENVALUES AND SINGULAR VALUES FOR TWO OR MORE MATRICES 362 5.13 FACTS
ON MATRIX PENCILS 369 5.14 FACTS ON MATRIX EIGENSTRUCTURE 369 5.15 FACTS
ON MATRIX FACTORIZATIONS 377 5.16 FACTS ON COMPANION, VANDERMONDE,
CIRCULANT, AND HADAMARD MATRICES 385 5.17 FACTS ON SIMULTANEOUS
TRANSFORMATIONS 391 5.18 FACTS ON THE POLAR DECOMPOSITION 393 5.19 FACTS
ON ADDITIVE DECOMPOSITIONS 394 5.20 NOTES 396 6. GENERALIZED INVERSES
397 6.1 MOORE-PENROSE GENERALIZED INVERSE 397 6.2 DRAZIN GENERALIZED
INVERSE 401 6.3 FACTS ON THE MOORE-PENROSE GENERALIZED INVERSE FOR ONE
MATRIX 404 6.4 FACTS ON THE MOORE-PENROSE GENERALIZED INVERSE FOR TWO OR
MORE MATRICES 411 6.5 FACTS ON THE MOORE-PENROSE GENERALIZED INVERSE FOR
PARTITIONED MATRICES 422 6.6 FACTS ON THE DRAZIN AND GROUP GENERALIZED
INVERSES 431 6.7 NOTES 438 XII CONTENTS 7. KRONECKER AND SCHUR ALGEBRA
439 7.1 KRONECKER PRODUCT 439 7.2 KRONECKER SUM AND LINEAR MATRIX
EQUATIONS 443 7.3 SCHUR PRODUCT 444 7.4 FACTS ON THE KRONECKER PRODUCT
445 7.5 FACTS ON THE KRONECKER SUM 450 7.6 FACTS ON THE SCHUR PRODUCT
454 7.7 NOTES 458 8. POSITIVE-SEMIDEFINITE MATRICES 459 8.1
POSITIVE-SEMIDEFINITE AND POSITIVE-DEFINITE ORDERINGS 459 8.2
SUBMATRICES 461 8.3 SIMULTANEOUS DIAGONALIZATION 465 8.4 EIGENVALUE
INEQUALITIES 467 8.5 EXPONENTIAL, SQUARE ROOT, AND LOGARITHM OF
HERMITIAN MATRICES 473 8.6 MATRIX INEQUALITIES 474 8.7 FACTS ON RANGE
AND RANK 486 8.8 FACTS ON STRUCTURED POSITIVE-SEMIDEFINITE MATRICES 488
8.9 FACTS ON IDENTITIES AND INEQUALITIES FOR ONE MATRIX 495 8.10 FACTS
ON IDENTITIES AND INEQUALITIES FOR TWO OR MORE MATRICES 501 8.11 FACTS
ON IDENTITIES AND INEQUALITIES FOR PARTITIONED MATRICES 514 8.12 FACTS
ON THE TRACE 523 8.13 FACTS ON THE DETERMINANT 533 8.14 FACTS ON CONVEX
SETS AND CONVEX FUNCTIONS 543 8.15 FACTS ON QUADRATIC FORMS 550 8.16
FACTS ON THE GAUSSIAN DENSITY 556 8.17 FACTS ON SIMULTANEOUS
DIAGONALIZATION 558 8.18 FACTS ON EIGENVALUES AND SINGULAR VALUES FOR
ONE MATRIX 559 8.19 FACTS ON EIGENVALUES AND SINGULAR VALUES FOR TWO OR
MORE MATRICES 564 8.20 FACTS ON ALTERNATIVE PARTIAL ORDERINGS 574 8.21
FACTS ON GENERALIZED INVERSES 577 8.22 FACTS ON THE KRONECKER AND SCHUR
PRODUCTS 584 8.23 NOTES 595 9. NORMS 597 9.1 VECTOR NORMS 597 9.2 MATRIX
NORMS 601 9.3 COMPATIBLE NORMS 604 9.4 INDUCED NORMS 607 9.5 INDUCED
LOWER BOUND 613 9.6 SINGULAR VALUE INEQUALITIES 615 9.7 FACTS ON VECTOR
NORMS 618 9.8 FACTS ON MATRIX NORMS FOR ONE MATRIX 627 9.9 FACTS ON
MATRIX NORMS FOR TWO OR MORE MATRICES 636 9.10 FACTS ON MATRIX NORMS FOR
PARTITIONED MATRICES 649 9.11 FACTS ON MATRIX NORMS AND EIGENVALUES FOR
ONE MATRIX 653 9.12 FACTS ON MATRIX NORMS AND EIGENVALUES FOR TWO OR
MORE MATRICES 656 9.13 FACTS ON MATRIX NORMS AND SINGULAR VALUES FOR ONE
MATRIX 659 CONTENTS XIII 9.14 FACTS ON MATRIX NORMS AND SINGULAR VALUES
FOR TWO OR MORE MATRICES 665 9.15 FACTS ON LINEAR EQUATIONS AND LEAST
SQUARES 676 9.16 NOTES 680 10. FUNCTIONS OF MATRICES AND THEIR
DERIVATIVES 681 10.1 OPEN SETS AND CLOSED SETS 681 10.2 LIMITS 682 10.3
CONTINUITY 684 10.4 DERIVATIVES 685 10.5 FUNCTIONS OF A MATRIX 688 10.6
MATRIX SQUARE ROOT AND MATRIX SIGN FUNCTIONS 690 10.7 MATRIX DERIVATIVES
690 10.8 FACTS ON ONE SET 693 10.9 FACTS ON TWO OR MORE SETS 695 10.10
FACTS ON MATRIX FUNCTIONS 698 10.11 FACTS ON FUNCTIONS 699 10.12 FACTS
ON DERIVATIVES 701 10.13 FACTS ON INFINITE SERIES 704 10.14 NOTES 705 11
. THE MATRIX EXPONENTIAL AND STABILITY THEORY 707 11 .1 DEFINITION OF
THE MATRIX EXPONENTIAL 707 11.2 STRUCTURE OF THE MATRIX EXPONENTIAL 710
11.3 EXPLICIT EXPRESSIONS 715 11.4 MATRIX LOGARITHMS 718 11.5 PRINCIPAL
LOGARITHM 720 11.6 LIE GROUPS 722 11.7 LYAPUNOV STABILITY THEORY 725
11.8 LINEAR STABILITY THEORY 726 11.9 THE LYAPUNOV EQUATION 730 11.10
DISCRETE-TIME STABILITY THEORY 734 11.11 FACTS ON MATRIX EXPONENTIAL
FORMULAS 736 11.12 FACTS ON THE MATRIX SINE AND COSINE 742 11.13 FACTS
ON THE MATRIX EXPONENTIAL FOR ONE MATRIX 743 11.14 FACTS ON THE MATRIX
EXPONENTIAL FOR TWO OR MORE MATRICES 746 11.15 FACTS ON THE MATRIX
EXPONENTIAL AND EIGENVALUES, SINGULAR VALUES, AND NORMS FOR ONE MATRIX
756 11.16 FACTS ON THE MATRIX EXPONENTIAL AND EIGENVALUES, SINGULAR
VALUES, AND NORMS FOR TWO OR MORE MATRICES 759 11.17 FACTS ON STABLE
POLYNOMIALS 763 11.18 FACTS ON STABLE MATRICES 766 11.19 FACTS ON ALMOST
NONNEGATIVE MATRICES 774 11.20 FACTS ON DISCRETE-TIME-STABLE POLYNOMIALS
777 11.21 FACTS ON DISCRETE-TIME-STABLE MATRICES 782 11.22 FACTS ON LIE
GROUPS 786 11.23 FACTS ON SUBSPACE DECOMPOSITION 786 11.24 NOTES 793 XIV
CONTENTS 12. LINEAR SYSTEMS AND CONTROL THEORY 795 12.1 STATE SPACE AND
TRANSFER FUNCTION MODELS 795 12.2 LAPLACE TRANSFORM ANALYSIS 798 12.3
THE UNOBSERVABLE SUBSPACE AND OBSERVABILITY 800 12.4 OBSERVABLE
ASYMPTOTIC STABILITY 805 12.5 DETECTABILITY 807 12.6 THE CONTROLLABLE
SUBSPACE AND CONTROLLABILITY 808 12.7 CONTROLLABLE ASYMPTOTIC STABILITY
816 12.8 STABILIZABILITY 820 12.9 REALIZATION THEORY 822 12.10 ZEROS 830
12.11 H 2 SYSTEM NORM 838 12.12 HARMONIC STEADY-STATE RESPONSE 841 12.13
SYSTEM INTERCONNECTIONS 842 12.14 STANDARD CONTROL PROBLEM 845 12.15
LINEAR-QUADRATIC CONTROL 847 12.16 SOLUTIONS OF THE RICCATI EQUATION 850
12.17 THE STABILIZING SOLUTION OF THE RICCATI EQUATION 855 12.18 THE
MAXIMAL SOLUTION OF THE RICCATI EQUATION 859 12.19 POSITIVE-SEMIDEFINITE
AND POSITIVE-DEFINITE SOLUTIONS OF THE RICCATI EQUATION 862 12.20 FACTS
ON STABILITY, OBSERVABILITY, AND CONTROLLABILITY 863 12.21 FACTS ON THE
LYAPUNOV EQUATION AND INERTIA 866 12.22 FACTS ON REALIZATIONS AND THE H
2 SYSTEM NORM 872 12.23 FACTS ON THE RICCATI EQUATION 875 12.24 NOTES
879 BIBLIOGRAPHY 881 AUTHOR INDEX 967 INDEX 979
|
| any_adam_object | 1 |
| author | Bernstein, Dennis S. 1954- |
| author_GND | (DE-588)140693319 |
| author_facet | Bernstein, Dennis S. 1954- |
| author_role | aut |
| author_sort | Bernstein, Dennis S. 1954- |
| author_variant | d s b ds dsb |
| building | Verbundindex |
| bvnumber | BV035768410 |
| classification_rvk | SK 220 |
| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)603342229 (DE-599)GBV574754105 |
| dewey-full | 512.9434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9434 |
| dewey-search | 512.9434 |
| dewey-sort | 3512.9434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035768410 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:05Z |
| institution | BVB |
| isbn | 9780691140391 9780691132877 |
| language | English |
| lccn | 2008036257 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018628177 |
| oclc_num | 603342229 |
| open_access_boolean | |
| owner | DE-634 DE-20 DE-83 DE-91G DE-BY-TUM DE-188 DE-384 DE-824 DE-703 DE-739 |
| owner_facet | DE-634 DE-20 DE-83 DE-91G DE-BY-TUM DE-188 DE-384 DE-824 DE-703 DE-739 |
| physical | XXXIX, 1139 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Bernstein, Dennis S. 1954- Verfasser (DE-588)140693319 aut Matrix mathematics theory, facts, and formulas Dennis S. Bernstein 2. ed. Princeton, NJ [u.a.] Princeton Univ. Press 2009 XXXIX, 1139 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Determinante (DE-588)4138983-9 gnd rswk-swf Matrizenpolynom (DE-588)4169130-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Lineare Kontrolltheorie (DE-588)4123657-9 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Matrizentheorie (DE-588)4128970-5 s Matrix Mathematik (DE-588)4037968-1 s Determinante (DE-588)4138983-9 s Matrizenpolynom (DE-588)4169130-1 s Lineares Gleichungssystem (DE-588)4035826-4 s Lineare Kontrolltheorie (DE-588)4123657-9 s Matrizenrechnung (DE-588)4126963-9 s DE-604 Gefolgt von Scalar, vector, and matrix mathematics 978-0-691-15120-5 (DE-604)BV044925277 http://www.gbv.de/dms/ilmenau/toc/574754105.PDF lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bernstein, Dennis S. 1954- Matrix mathematics theory, facts, and formulas Matrizentheorie (DE-588)4128970-5 gnd Determinante (DE-588)4138983-9 gnd Matrizenpolynom (DE-588)4169130-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4128970-5 (DE-588)4138983-9 (DE-588)4169130-1 (DE-588)4035826-4 (DE-588)4123657-9 (DE-588)4037968-1 (DE-588)4126963-9 (DE-588)4123623-3 |
| title | Matrix mathematics theory, facts, and formulas |
| title_auth | Matrix mathematics theory, facts, and formulas |
| title_exact_search | Matrix mathematics theory, facts, and formulas |
| title_full | Matrix mathematics theory, facts, and formulas Dennis S. Bernstein |
| title_fullStr | Matrix mathematics theory, facts, and formulas Dennis S. Bernstein |
| title_full_unstemmed | Matrix mathematics theory, facts, and formulas Dennis S. Bernstein |
| title_new | Scalar, vector, and matrix mathematics |
| title_short | Matrix mathematics |
| title_sort | matrix mathematics theory facts and formulas |
| title_sub | theory, facts, and formulas |
| topic | Matrizentheorie (DE-588)4128970-5 gnd Determinante (DE-588)4138983-9 gnd Matrizenpolynom (DE-588)4169130-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Lineare Kontrolltheorie (DE-588)4123657-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Matrizentheorie Determinante Matrizenpolynom Lineares Gleichungssystem Lineare Kontrolltheorie Matrix Mathematik Matrizenrechnung Lehrbuch |
| url | http://www.gbv.de/dms/ilmenau/toc/574754105.PDF http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628177&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bernsteindenniss matrixmathematicstheoryfactsandformulas |
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