Matrix operations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
McGraw-Hill
2011
|
| Edition: | 2. ed. |
| Series: | Schaum's outline series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. u.d.T.: Broson, Richard: Schaum's outline of theory and problems of matrix operations |
| Physical Description: | 230 S. |
| ISBN: | 9780071756044 |
Staff View
MARC
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| 100 | 1 | |a Bronson, Richard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matrix operations |
| 250 | |a 2. ed. | ||
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Record in the Search Index
| _version_ | 1804149374124556288 |
|---|---|
| adam_text | Contents
Chapter
1 BASIC
OPERATIONS
.....................................
Matrices. Vectors and dot products. Matrix addition and matrix
subtraction. Scalar multiplication and matrix multiplication. Row-echelon
form. Elementary row and column operations. Rank.
Chapter
2
SIMULTANEOUS LINEAR EQUATIONS
................
Consistency. Matrix notation. Theory of solutions. Simplifying
operations. Gaussian elimination algorithm. Pivoting strategies.
11
Chapter
3
SQUARE MATRICES
......................................
Diagonals. Elementary matrices.
LU
decomposition. Simultaneous linear
equations. Powers of a matrix.
24
Chapter
4
MATRIX INVERSION
.....................
The inverse. Simple inverses. Calculating inverses,
equations. Properties of the inverse.
34
Simultaneous linear
Chapter
5
DETERMINANTS.
. .
Expansion by cofactors,
partitioned matrices.
Properties of determinants. Determinants of
Pivotal condensation. Inversion by determinants.
42
Chapter
6
VECTORS
..............................................
Dimension. Linear dependence and independence. Linear combinations.
Properties of linearly dependent vectors. Row rank and column rank.
52
Chapter
7
EIGENVALUES AND EIGENVECTORS
.........................
Characteristic equation. Properties of eigenvalues and eigenvectors. Linearly
independent eigenvectors. Computational considerations. The Cayley-
Hamilton theorem.
60
Chapter
8
FUNCTIONS OF MATRICES
................................
Sequences and series of matrices. Well-defined functions. Computing
functions of matrices. The function eK . Differentiation and integration of
matrices. Differential equations. The matrix equation AX
+
XB
=
С
71
CONTENTS
Chapter
9
CANONICAL BASES
........................................ 82
Generalized eigenvectors. Chains. Canonical basis. The minimum
polynomial.
Chapter
10
SIMILARITY
.............................................. 91
Similar matrices. Modal matrix. Jordan canonical form. Similarity and
Jordan canonical form. Functions of matrices.
Chapter
11
INNER PRODUCTS
......................................... 103
Complex conjugates. The inner product. Properties of inner products.
Orthogonality. Gram-Schmidt orthogonalization.
Chapter
12
NORMS
................................................... 110
Vector norms. Normalized vectors and distance. Matrix norms. Induced
norms. Compatibility. Spectral radius.
Chapter
13
HERMITIAN MATRICES
.................................... 119
Normal matrices. Hermitian matrices. Real symmetric matrices. The
adjoint. Self-adjoint matrices.
Chapter
14
POSITIVE DEFINITE MATRICES
............................. 128
Definite matrices. Tests for positive definiteness. Square roots of
matrices. Cholesky decomposition.
Chapter
15
UNITARY TRANSFORMATIONS
.............................. 136
Unitary matrices.
Schur
decomposition. Elementary reflectors. Summary of
similarity transformations.
Chapter
16
QUADRATIC FORMS AND CONGRUENCE
.....................
I44
Quadratic form. Diagonal form. Congruence. Inertia. Rayleigh quotient.
Chapter
17
NONNEGATIVE MATRICES
.................................
I52
Nonnegative
and positive matrices. Irreducible matrices. Primitive
matrices. Stochastic matrices. Finite Markov chains.
Chapter
18
PATTERNED MATRICES
....____.......____..................... .... 160
Circulant
matrices. Band matrices. Tridiagonal matrices.
Hessenberg form.
CONTENTS
Chapter
19 POWER
METHODS FOR LOCATING REAL EIGENVALUES
...... 169
Numerical methods. The power method. The inverse power method. The
shifted inverse power method. Gerschgorin s theorem.
Chapter
20
THE QR ALGORITHM
...................................... 181
The modified Gram-Schmidt process. QR decomposition. The QR
algorithm. Accelerating convergence.
Chapter
21
GENERALIZED INVERSES
.................................. 192
Properties. A formula for generalized inverses. Singular-value
decomposition. A stable formula for the generalized inverse. Least-squares
solutions.
ANSWERS TO SUPPLEMENTARY PROBLEMS
............................... 203
INDEX.
................................................................ 227
|
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| classification_tum | MAT 150f |
| ctrlnum | (OCoLC)812200118 (DE-599)HBZHT016767767 |
| discipline | Mathematik Wirtschaftswissenschaften |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:22:01Z |
| institution | BVB |
| isbn | 9780071756044 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025195103 |
| oclc_num | 812200118 |
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| owner_facet | DE-473 DE-BY-UBG |
| physical | 230 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | Schaum's outline series |
| spelling | Bronson, Richard Verfasser aut Matrix operations 2. ed. New York [u.a.] McGraw-Hill 2011 230 S. txt rdacontent n rdamedia nc rdacarrier Schaum's outline series 1. Aufl. u.d.T.: Broson, Richard: Schaum's outline of theory and problems of matrix operations Matrices Matrizenrechnung (DE-588)4126963-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Matériel didactique Matrizenrechnung (DE-588)4126963-9 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025195103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bronson, Richard Matrix operations Matrices Matrizenrechnung (DE-588)4126963-9 gnd |
| subject_GND | (DE-588)4126963-9 (DE-588)4143389-0 |
| title | Matrix operations |
| title_auth | Matrix operations |
| title_exact_search | Matrix operations |
| title_full | Matrix operations |
| title_fullStr | Matrix operations |
| title_full_unstemmed | Matrix operations |
| title_short | Matrix operations |
| title_sort | matrix operations |
| topic | Matrices Matrizenrechnung (DE-588)4126963-9 gnd |
| topic_facet | Matrices Matrizenrechnung Aufgabensammlung Matériel didactique |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025195103&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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