Linear algebra and matrix computations with MATLAB:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2020]
[Beijing] Tsinghua University Press |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XI, 289 Seiten Illustrationen, Diagramme 24 cm, 521 g |
| ISBN: | 9783110663631 3110663635 |
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MARC
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| 020 | |a 9783110663631 |c Broschur : EUR 59.95 (DE) (freier Preis), EUR 59.95 (AT) (freier Preis) |9 978-3-11-066363-1 | ||
| 020 | |a 3110663635 |9 3-11-066363-5 | ||
| 024 | 3 | |a 9783110663631 | |
| 035 | |a (OCoLC)1110094940 | ||
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| 044 | |a gw |c XA-DE-BE | ||
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| 084 | |a ST 601 |0 (DE-625)143682: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Xue, Dingyu |e Verfasser |0 (DE-588)1098160967 |4 aut | |
| 245 | 1 | 0 | |a Linear algebra and matrix computations with MATLAB |c Dingyü Xue |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 1 | |a [Beijing] |b Tsinghua University Press | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XI, 289 Seiten |b Illustrationen, Diagramme |c 24 cm, 521 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a MATLAB |0 (DE-588)4329066-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | 1 | |a MATLAB |0 (DE-588)4329066-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-066699-1 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-066371-6 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1190750600/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032185105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032185105 | ||
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| _version_ | 1804181553364860928 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
1
INTRODUCTION
TO
LINEAR
ALGEBRA
AND
MATRIX
COMPUTATION
*
1
1.1
MATRICES
AND
LINEAR
EQUATIONS
*
1
1.1.1
MATRIX
REPRESENTATION
OF
TABLES
*
1
1.1.2
MODELING
AND
SOLVING
LINEAR
EQUATIONS
*
3
1.2
INTRODUCTION
OF
LINEAR
ALGEBRA
*
8
1.2.1
MATHEMATICAL
DEVELOPMENT
OF
LINEAR
ALGEBRA
*
8
1.2.2
NUMERICAL
LINEAR
ALGEBRA
*
10
1.3
OUTLINE
OF
THE
BOOK
*
10
1.4
EXERCISES
OF
THE
CHAPTER
*
12
2
REPRESENTATION
AND
FUNDAMENTAL
COMPUTATIONS
OF
MATRICES
*
13
2.1
INPUT
OF
AN
ORDINARY
MATRIX
*
13
2.2
INPUT
OF
SPECIAL
MATRICES
*
15
2.2.1
MATRICES
OF
ZEROS,
ONES,
AND
IDENTITY
MATRICES
*
15
2.2.2
MATRICES
WITH
RANDOM
ELEMENTS
*
16
2.2.3
HANKEL
MATRIX
*
18
2.2.4
DIAGONAL
MATRICES
*
19
2.2.5
HILBERT
MATRIX
AND
ITS
INVERSE
*
22
2.2.6
COMPANION
MATRICES
*
22
2.2.7
VANDERMONDE
MATRICES
*
23
2.2.8
SOME
COMMONLY
USED
TEST
MATRICES
*
24
2.3
SYMBOLIC
MATRIX
INPUT
*
26
2.3.1
INPUT
OF
SPECIAL
SYMBOLIC
MATRICES
*
26
2.3.2
GENERATING
ARBITRARY
CONSTANT
MATRICES
*
27
2.3.3
ARBITRARY
MATRIX
FUNCTION
INPUT
*
28
2.4
INPUT
OF
SPARSE
MATRICES
*
29
2.5
FUNDAMENTAL
MATRIX
COMPUTATIONS
*
32
2.5.1
HANDLING
COMPLEX
MATRICES
*
32
2.5.2
TRANSPOSITION
AND
ROTATION
OF
MATRICES
*
33
2.5.3
ALGEBRAIC
COMPUTATION
OF
MATRICES
*
35
2.5.4
KRONECKER
PRODUCTS
AND
SUMS
*
39
2.6
CALCULUS
COMPUTATIONS
WITH
MATRICES
*
40
2.6.1
MATRIX
D
ERIVATIVES
----
41
2.6.2
INTEGRALS
OF
MATRIX
FUNCTIONS
-----42
2.6.3
JACOBIAN
MATRICES
OF
VECTOR
FUNCTIONS
*
43
2.6.4
HESSIAN
MATRICES
-----
43
2.7
EXERCISES
-----
44
VIII
*
CONTENTS
3
3.1
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.5
3.5.1
3.5.2
3.5.3
3.6
FUNDAMENTAL
ANALYSIS
OF
MATRICES
*
47
DETERMINANTS
*
47
DETERMINANT
DEFINITION
AND
PROPERTIES
-----
47
DETERMINANTS
OF
SMALL-SCALE
MATRICES
*
48
MATLAB
SOLUTION
OF
DETERMINANT
PROBLEMS
-----
52
DETERMINANTS
OF
SPECIAL
MATRICES
OF
ANY
SIZES
*
55
CRAMER
*
S
RULE
IN
LINEAR
EQUATIONS
*
57
POSITIVE
AND
TOTALLY
POSITIVE
MATRICES
*
59
SIMPLE
ANALYSIS
OF
MATRICES
*
60
THE
TRACES
-----
60
LINEAR
INDEPENDENCE
AND
MATRIX
RANK
-----
61
NORMS
-----
63
VECTOR
SPACE
*
65
INVERSE
AND
GENERALIZED
INVERSE
MATRICES
*
66
INVERSE
MATRICES
*
66
DERIVATIVES
OF
INVERSE
MATRIX
-----
68
MATLAB
BASED
INVERSE
MATRIX
EVALUATION
-----
69
REDUCED
ROW
ECHELON
FORM
-----
72
GENERALIZED
INVERSE
-----
74
CHARACTERISTIC
POLYNOMIALS
AND
EIGENVALUES
*
77
CHARACTERISTIC
POLYNOMIALS
-----
77
FINDING
THE
ROOTS
OF
POLYNOMIAL
EQUATIONS
-----
79
EIGENVALUES
AND
EIGENVECTORS
*
80
GENERALIZED
EIGENVALUES
AND
EIGENVECTORS
*
84
GERSHGORIN
DISCS
AND
DIAGONALLY
DOMINANT
MATRICES
*
86
MATRIX
POLYNOMIALS
-----
87
SOLUTIONS
OF
MATRIX
POLYNOMIAL
PROBLEMS
*
88
MINIMAL
POLYNOMIALS
OF
MATRICES
*
89
CONVERSIONS
BETWEEN
SYMBOLIC
AND
NUMERICAL
POLYNOMIALS
*
90
PROBLEMS
*
92
4
4.1
4.1.1
4.1.2
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
FUNDAMENTAL
TRANSFORMATION
AND
DECOMPOSITION
OF
MATRICES
*
95
SIMILARITY
TRANSFORM
AND
ORTHOGONAL
MATRICES
*
95
SIMILARITY
TRANSFORM
-----
95
ORTHOGONAL
MATRICES
AND
ORTHONORMAL
BASES
*
96
ELEMENTARY
ROW
TRANSFORMS
-----
98
THREE
TYPES
OF
ELEMENTARY
ROW
TRANSFORMS
*
98
INVERSE
THROUGH
ELEMENTARY
ROW
TRANSFORMS
*
100
COMPUTING
INVERSES
WITH
PIVOT
METHODS
-----
102
TRIANGULAR
DECOMPOSITION
OF
MATRICES
*
103
GAUSSIAN
ELIMINATION
OF
LINEAR
EQUATIONS
*
103
TRIANGULAR
FACTORIZATION
AND
IMPLEMENTATION
-----
105
CONTENTS
*
IX
4.3.3
MATLAB
TRIANGULAR
FACTORIZATION
SOLVER
-----
106
4.4
CHOLESKY
FACTORIZATION
-----
108
4.4.1
CHOLESKY
FACTORIZATION
OF
SYMMETRIC
MATRICES
-----
108
4.4.2
QUADRATIC
FORMS
OF
SYMMETRIC
MATRICES
-----
109
4.4.3
POSITIVE
DEFINITE
AND
REGULAR
MATRICES
-----
110
4.4.4
CHOLESKY
FACTORIZATION
OF
NONPOSITIVE
DEFINITE
MATRICES
*
112
4.5
COMPANION
AND
JORDAN
TRANSFORMS
------
113
4.5.1
COMPANION
FORM
TRANSFORMATION
-----
113
4.5.2
MATRIX
DIAGONALIZATION
-----
114
4.5.3
JORDAN
TRANSFORM
-----
115
4.5.4
REAL
JORDAN
TRANSFORMS
FOR
MATRICES
WITH
REPEATED
COMPLEX
EIGENVALUES
*
117
4.5.5
SIMULTANEOUS
DIAGONALIZATION
*
119
4.6
SINGULAR
VALUE
DECOMPOSITION
*
120
4.6.1
SINGULAR
VALUES
AND
CONDITION
NUMBERS
*
121
4.6.2
SINGULAR
VALUE
DECOMPOSITION
OF
RECTANGULAR
MATRICES
-----
123
4.6.3
SVD
BASED
SIMULTANEOUS
DIAGONALIZATION
*
124
4.7
GIVENS
AND
HOUSEHOLDER
TRANSFORMS
-----
125
4.7.1
TWO-DIMENSIONAL
COORDINATE
ROTATION
TRANSFORM
-----
125
4.7.2
GIVENS
TRANSFORM
OF
ORDINARY
MATRICES
-----
128
4.7.3
HOUSEHOLDER
TRANSFORM
-----
130
4.8
PROBLEMS
-----
131
5
SOLUTIONS
OF
MATRIX
EQUATIONS
*
135
5.1
LINEAR
EQUATIONS
*
135
5.1.1
UNIQUE
SOLUTIONS
------
136
5.1.2
LINEAR
EQUATIONS
WITH
INFINITELY
MANY
SOLUTIONS
-----
140
5.1.3
INCONSISTENT
SYSTEMS
OF
EQUATIONS
-----
143
5.1.4
GRAPHICAL
INTERPRETATION
OF
LINEAR
SOLUTIONS
*
144
5.2
OTHER
FORMS
OF
SIMPLE
LINEAR
EQUATIONS
*
146
5.2.1
XA
-
B
EQUATIONS
-----
146
5.2.2
AXB
-
C
EQUATIONS
-----
148
5.2.3
KRONECKER
PRODUCT-BASED
SOLUTIONS
-----
150
5.2.4
MULTITERM
AXB
=
C
EQUATIONS
-----
151
5.3
LYAPUNOV
EQUATIONS
------
152
5.3.1
CONTINUOUS
LYAPUNOV
EQUATIONS
*
152
5.3.2
2X2
LYAPUNOV
EQUATIONS
-----
154
5.3.3
ANALYTICAL
SOLUTION
OF
LYAPUNOV
EQUATIONS
-----
155
5.3.4
STEIN
EQUATIONS
-----
156
5.3.5
DISCRETE
LYAPUNOV
EQUATION
*
157
5.4
SYLVESTER
EQUATIONS
-----
158
5.4.1
NUMERICAL
SOLUTIONS
OF
SYLVESTER
EQUATIONS
*
158
X
*
CONTENTS
5.4.2
ANALYTICAL
SOLUTION
OF
SYLVESTER
EQUATION
-----
159
5.4.3
SYLVESTER
EQUATIONS
WITH
CONSTANT
PARAMETERS
*
161
5.4.4
MULTITERM
SYLVESTER
EQUATIONS
-----
162
5.5
NONLINEAR
MATRIX
EQUATIONS
-----
163
5.5.1
RICCATI
EQUATIONS
-----
163
5.5.2
SOLUTIONS
OF
GENERAL
NONLINEAR
EQUATIONS
*
165
5.5.3
VARIATIONS
OF
RICCATI
EQUATIONS
-----
169
5.5.4
NUMERICAL
SOLUTIONS
OF
NONLINEAR
MATRIX
EQUATIONS
*
170
5.6
DIOPHANTINE
EQUATIONS
-----
171
5.6.1
COPRIMENESS
OF
POLYNOMIALS
-----
172
5.6.2
DIOPHANTINE
POLYNOMIAL
EQUATIONS
*
172
5.6.3
SOLUTIONS
OF
PSEUDO-POLYNOMIAL
EQUATIONS
175
5.7
PROBLEMS
-----
176
6
MATRIX
FUNCTIONS
*
181
6.1
NONLINEAR
COMPUTATION
OF
MATRIX
ELEMENTS
*
182
6.1.1
INTEGER
ROUNDING
AND
RATIONALIZATION
-----
182
6.1.2
TRANSCENDENTAL
FUNCTION
COMPUTATIONS
-----
183
6.1.3
VECTOR
SORTING,
MINIMIZATION,
AND
MAXIMIZATION
-----
187
6.1.4
MEANS,
VARIANCES,
AND
STANDARD
DEVIATIONS
*
188
6.2
MATRIX
EXPONENTIALS
-----
189
6.2.1
DEFINITIONS
AND
PROPERTIES
OF
MATRIX
FUNCTIONS
-----
189
6.2.2
COMPUTING
MATRIX
EXPONENTIALS
*
190
6.2.3
TAYLOR
SERIES-BASED
TRUNCATION
ALGORITHM
*
190
6.2.4
A
CAYLEY-HAMILTON
THEOREM-BASED
ALGORITHM
*
192
6.2.5
DIRECT
MATLAB
SOLVER
-----
193
6.2.6
JORDAN
TRANSFORM-BASED
APPROACH
*
195
6.3
MATRIX
LOGARITHMIC
AND
SQUARE
ROOT
FUNCTIONS
*
196
6.3.1
MATRIX
LOGARITHMIC
FUNCTION
-----
196
6.3.2
SQUARE
ROOT
OF
A
MATRIX
-----
198
6.4
MATRIX
TRIGONOMETRIC
FUNCTIONS
-----
199
6.4.1
COMPUTATION
OF
MATRIX
TRIGONOMETRIC
FUNCTIONS
*
199
6.4.2
POWER
SERIES-BASED
TRIGONOMETRIC
FUNCTION
EVALUATION
*
200
6.4.3
ANALYTICAL
EVALUATIONS
OF
MATRIX
TRIGONOMETRIC
FUNCTIONS
*
202
6.5
ARBITRARY
MATRIX
FUNCTIONS
--------
204
6.5.1
NILPOTENT
MATRICES
-----
204
6.5.2
JORDAN
TRANSFORM-BASED
MATRIX
FUNCTION
EVALUATIONS
*
205
6.5.3
USER-DEFINED
MATRIX
FUNCTIONS
*
208
6.6
MATRIX
POWERS
-----
210
6.6.1
MATRIX
POWERS
VIA
JORDAN
TRANSFORM
-----
210
6.6.2
A
MATRIX
POWER
SOLVER
-----
211
6.6.3
MATRIX
POWERS
VIA
THE
Z
TRANSFORM
-----
213
CONTENTS
*
XI
6.6.4
6.7
COMPUTING
-----
214
PROBLEMS
-----
215
7
7.1
7.1.1
7.1.2
7.1.3
7.2
7.2.1
7.2.2
7.2.3
7.2.4
7.3
7.3.1
7.3.2
7.3.3
7.3.4
7.4
7.4.1
7.4.2
7.4.3
7.5
7.5.1
7.5.2
7.5.3
7.5.4
7.5.5
7.6
7.6.1
7.6.2
7.6.3
7.6.4
7.6.5
7.7
LINEAR
ALGEBRA
APPLICATIONS
*
217
LINEAR
EQUATIONS
APPLICATIONS
-----
217
ELECTRIC
NETWORK
ANALYSIS
*
217
ANALYSIS
OF
TRUSS
STRUCTURES
-----
224
BALANCING
CHEMICAL
REACTION
EQUATIONS
-----
224
APPLICATIONS
IN
LINEAR
CONTROL
SYSTEMS
-----
227
CONTROL
SYSTEM
MODEL
CONVERSIONS
-----
227
QUALITATIVE
ANALYSIS
OF
LINEAR
SYSTEMS
*
229
TRANSMISSION
ZEROS
IN
MULTIVARIATE
SYSTEMS
-----
231
DIRECT
SOLUTIONS
OF
LINEAR
DIFFERENTIAL
EQUATIONS
-----
232
INTRODUCTION
TO
DIGITAL
IMAGE
PROCESSING
*
233
IMAGE
INPUT
AND
DISPLAY
-----
234
SINGULAR
VALUE
DECOMPOSITION
APPLICATIONS
*
235
RESIZING
AND
ROTATING
IMAGES
-----
237
IMAGE
ENHANCEMENT
*
239
GRAPH
THEORY
AND
APPLICATIONS
-----
241
ORIENTED
GRAPH
DESCRIPTIONS
-----
242
DIJKSTRA
ALGORITHM
AND
APPLICATIONS
-----
244
SIMPLIFICATION
OF
CONTROL
SYSTEM
BLOCK
DIAGRAMS
*
247
SOLVING
DIFFERENCE
EQUATIONS
-----
251
ANALYTICAL
SOLUTIONS
-----
252
NUMERICAL
SOLUTIONS
OF
LINEAR
TIME-VARYING
DIFFERENCE
EQUATIONS
*
254
LINEAR
TIME-INVARIANT
DIFFERENCE
EQUATIONS
*
255
NUMERICAL
SOLUTIONS
OF
NONLINEAR
DIFFERENCE
EQUATIONS
*
257
MARKOV
CHAIN
SIMULATION
----
258
DATA
FITTING
AND
ANALYSIS
-----
260
LINEAR
REGRESSION
-----
261
POLYNOMIAL
FITTING
----
264
CHEBYSHEV
POLYNOMIALS
*
265
BEZIER
CURVES
-----
267
PRINCIPAL
COMPONENT
ANALYSIS
*
269
EXERCISES
OF
THE
CHAPTER
*
272
BIBLIOGRAPHY
*
279
MATLAB
FUNCTION
INDEX
*
281
INDEX
*
285
|
| adam_txt |
CONTENTS
PREFACE
*
V
1
INTRODUCTION
TO
LINEAR
ALGEBRA
AND
MATRIX
COMPUTATION
*
1
1.1
MATRICES
AND
LINEAR
EQUATIONS
*
1
1.1.1
MATRIX
REPRESENTATION
OF
TABLES
*
1
1.1.2
MODELING
AND
SOLVING
LINEAR
EQUATIONS
*
3
1.2
INTRODUCTION
OF
LINEAR
ALGEBRA
*
8
1.2.1
MATHEMATICAL
DEVELOPMENT
OF
LINEAR
ALGEBRA
*
8
1.2.2
NUMERICAL
LINEAR
ALGEBRA
*
10
1.3
OUTLINE
OF
THE
BOOK
*
10
1.4
EXERCISES
OF
THE
CHAPTER
*
12
2
REPRESENTATION
AND
FUNDAMENTAL
COMPUTATIONS
OF
MATRICES
*
13
2.1
INPUT
OF
AN
ORDINARY
MATRIX
*
13
2.2
INPUT
OF
SPECIAL
MATRICES
*
15
2.2.1
MATRICES
OF
ZEROS,
ONES,
AND
IDENTITY
MATRICES
*
15
2.2.2
MATRICES
WITH
RANDOM
ELEMENTS
*
16
2.2.3
HANKEL
MATRIX
*
18
2.2.4
DIAGONAL
MATRICES
*
19
2.2.5
HILBERT
MATRIX
AND
ITS
INVERSE
*
22
2.2.6
COMPANION
MATRICES
*
22
2.2.7
VANDERMONDE
MATRICES
*
23
2.2.8
SOME
COMMONLY
USED
TEST
MATRICES
*
24
2.3
SYMBOLIC
MATRIX
INPUT
*
26
2.3.1
INPUT
OF
SPECIAL
SYMBOLIC
MATRICES
*
26
2.3.2
GENERATING
ARBITRARY
CONSTANT
MATRICES
*
27
2.3.3
ARBITRARY
MATRIX
FUNCTION
INPUT
*
28
2.4
INPUT
OF
SPARSE
MATRICES
*
29
2.5
FUNDAMENTAL
MATRIX
COMPUTATIONS
*
32
2.5.1
HANDLING
COMPLEX
MATRICES
*
32
2.5.2
TRANSPOSITION
AND
ROTATION
OF
MATRICES
*
33
2.5.3
ALGEBRAIC
COMPUTATION
OF
MATRICES
*
35
2.5.4
KRONECKER
PRODUCTS
AND
SUMS
*
39
2.6
CALCULUS
COMPUTATIONS
WITH
MATRICES
*
40
2.6.1
MATRIX
D
ERIVATIVES
----
41
2.6.2
INTEGRALS
OF
MATRIX
FUNCTIONS
-----42
2.6.3
JACOBIAN
MATRICES
OF
VECTOR
FUNCTIONS
*
43
2.6.4
HESSIAN
MATRICES
-----
43
2.7
EXERCISES
-----
44
VIII
*
CONTENTS
3
3.1
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.1.6
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.5
3.5.1
3.5.2
3.5.3
3.6
FUNDAMENTAL
ANALYSIS
OF
MATRICES
*
47
DETERMINANTS
*
47
DETERMINANT
DEFINITION
AND
PROPERTIES
-----
47
DETERMINANTS
OF
SMALL-SCALE
MATRICES
*
48
MATLAB
SOLUTION
OF
DETERMINANT
PROBLEMS
-----
52
DETERMINANTS
OF
SPECIAL
MATRICES
OF
ANY
SIZES
*
55
CRAMER
*
S
RULE
IN
LINEAR
EQUATIONS
*
57
POSITIVE
AND
TOTALLY
POSITIVE
MATRICES
*
59
SIMPLE
ANALYSIS
OF
MATRICES
*
60
THE
TRACES
-----
60
LINEAR
INDEPENDENCE
AND
MATRIX
RANK
-----
61
NORMS
-----
63
VECTOR
SPACE
*
65
INVERSE
AND
GENERALIZED
INVERSE
MATRICES
*
66
INVERSE
MATRICES
*
66
DERIVATIVES
OF
INVERSE
MATRIX
-----
68
MATLAB
BASED
INVERSE
MATRIX
EVALUATION
-----
69
REDUCED
ROW
ECHELON
FORM
-----
72
GENERALIZED
INVERSE
-----
74
CHARACTERISTIC
POLYNOMIALS
AND
EIGENVALUES
*
77
CHARACTERISTIC
POLYNOMIALS
-----
77
FINDING
THE
ROOTS
OF
POLYNOMIAL
EQUATIONS
-----
79
EIGENVALUES
AND
EIGENVECTORS
*
80
GENERALIZED
EIGENVALUES
AND
EIGENVECTORS
*
84
GERSHGORIN
DISCS
AND
DIAGONALLY
DOMINANT
MATRICES
*
86
MATRIX
POLYNOMIALS
-----
87
SOLUTIONS
OF
MATRIX
POLYNOMIAL
PROBLEMS
*
88
MINIMAL
POLYNOMIALS
OF
MATRICES
*
89
CONVERSIONS
BETWEEN
SYMBOLIC
AND
NUMERICAL
POLYNOMIALS
*
90
PROBLEMS
*
92
4
4.1
4.1.1
4.1.2
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
FUNDAMENTAL
TRANSFORMATION
AND
DECOMPOSITION
OF
MATRICES
*
95
SIMILARITY
TRANSFORM
AND
ORTHOGONAL
MATRICES
*
95
SIMILARITY
TRANSFORM
-----
95
ORTHOGONAL
MATRICES
AND
ORTHONORMAL
BASES
*
96
ELEMENTARY
ROW
TRANSFORMS
-----
98
THREE
TYPES
OF
ELEMENTARY
ROW
TRANSFORMS
*
98
INVERSE
THROUGH
ELEMENTARY
ROW
TRANSFORMS
*
100
COMPUTING
INVERSES
WITH
PIVOT
METHODS
-----
102
TRIANGULAR
DECOMPOSITION
OF
MATRICES
*
103
GAUSSIAN
ELIMINATION
OF
LINEAR
EQUATIONS
*
103
TRIANGULAR
FACTORIZATION
AND
IMPLEMENTATION
-----
105
CONTENTS
*
IX
4.3.3
MATLAB
TRIANGULAR
FACTORIZATION
SOLVER
-----
106
4.4
CHOLESKY
FACTORIZATION
-----
108
4.4.1
CHOLESKY
FACTORIZATION
OF
SYMMETRIC
MATRICES
-----
108
4.4.2
QUADRATIC
FORMS
OF
SYMMETRIC
MATRICES
-----
109
4.4.3
POSITIVE
DEFINITE
AND
REGULAR
MATRICES
-----
110
4.4.4
CHOLESKY
FACTORIZATION
OF
NONPOSITIVE
DEFINITE
MATRICES
*
112
4.5
COMPANION
AND
JORDAN
TRANSFORMS
------
113
4.5.1
COMPANION
FORM
TRANSFORMATION
-----
113
4.5.2
MATRIX
DIAGONALIZATION
-----
114
4.5.3
JORDAN
TRANSFORM
-----
115
4.5.4
REAL
JORDAN
TRANSFORMS
FOR
MATRICES
WITH
REPEATED
COMPLEX
EIGENVALUES
*
117
4.5.5
SIMULTANEOUS
DIAGONALIZATION
*
119
4.6
SINGULAR
VALUE
DECOMPOSITION
*
120
4.6.1
SINGULAR
VALUES
AND
CONDITION
NUMBERS
*
121
4.6.2
SINGULAR
VALUE
DECOMPOSITION
OF
RECTANGULAR
MATRICES
-----
123
4.6.3
SVD
BASED
SIMULTANEOUS
DIAGONALIZATION
*
124
4.7
GIVENS
AND
HOUSEHOLDER
TRANSFORMS
-----
125
4.7.1
TWO-DIMENSIONAL
COORDINATE
ROTATION
TRANSFORM
-----
125
4.7.2
GIVENS
TRANSFORM
OF
ORDINARY
MATRICES
-----
128
4.7.3
HOUSEHOLDER
TRANSFORM
-----
130
4.8
PROBLEMS
-----
131
5
SOLUTIONS
OF
MATRIX
EQUATIONS
*
135
5.1
LINEAR
EQUATIONS
*
135
5.1.1
UNIQUE
SOLUTIONS
------
136
5.1.2
LINEAR
EQUATIONS
WITH
INFINITELY
MANY
SOLUTIONS
-----
140
5.1.3
INCONSISTENT
SYSTEMS
OF
EQUATIONS
-----
143
5.1.4
GRAPHICAL
INTERPRETATION
OF
LINEAR
SOLUTIONS
*
144
5.2
OTHER
FORMS
OF
SIMPLE
LINEAR
EQUATIONS
*
146
5.2.1
XA
-
B
EQUATIONS
-----
146
5.2.2
AXB
-
C
EQUATIONS
-----
148
5.2.3
KRONECKER
PRODUCT-BASED
SOLUTIONS
-----
150
5.2.4
MULTITERM
AXB
=
C
EQUATIONS
-----
151
5.3
LYAPUNOV
EQUATIONS
------
152
5.3.1
CONTINUOUS
LYAPUNOV
EQUATIONS
*
152
5.3.2
2X2
LYAPUNOV
EQUATIONS
-----
154
5.3.3
ANALYTICAL
SOLUTION
OF
LYAPUNOV
EQUATIONS
-----
155
5.3.4
STEIN
EQUATIONS
-----
156
5.3.5
DISCRETE
LYAPUNOV
EQUATION
*
157
5.4
SYLVESTER
EQUATIONS
-----
158
5.4.1
NUMERICAL
SOLUTIONS
OF
SYLVESTER
EQUATIONS
*
158
X
*
CONTENTS
5.4.2
ANALYTICAL
SOLUTION
OF
SYLVESTER
EQUATION
-----
159
5.4.3
SYLVESTER
EQUATIONS
WITH
CONSTANT
PARAMETERS
*
161
5.4.4
MULTITERM
SYLVESTER
EQUATIONS
-----
162
5.5
NONLINEAR
MATRIX
EQUATIONS
-----
163
5.5.1
RICCATI
EQUATIONS
-----
163
5.5.2
SOLUTIONS
OF
GENERAL
NONLINEAR
EQUATIONS
*
165
5.5.3
VARIATIONS
OF
RICCATI
EQUATIONS
-----
169
5.5.4
NUMERICAL
SOLUTIONS
OF
NONLINEAR
MATRIX
EQUATIONS
*
170
5.6
DIOPHANTINE
EQUATIONS
-----
171
5.6.1
COPRIMENESS
OF
POLYNOMIALS
-----
172
5.6.2
DIOPHANTINE
POLYNOMIAL
EQUATIONS
*
172
5.6.3
SOLUTIONS
OF
PSEUDO-POLYNOMIAL
EQUATIONS
175
5.7
PROBLEMS
-----
176
6
MATRIX
FUNCTIONS
*
181
6.1
NONLINEAR
COMPUTATION
OF
MATRIX
ELEMENTS
*
182
6.1.1
INTEGER
ROUNDING
AND
RATIONALIZATION
-----
182
6.1.2
TRANSCENDENTAL
FUNCTION
COMPUTATIONS
-----
183
6.1.3
VECTOR
SORTING,
MINIMIZATION,
AND
MAXIMIZATION
-----
187
6.1.4
MEANS,
VARIANCES,
AND
STANDARD
DEVIATIONS
*
188
6.2
MATRIX
EXPONENTIALS
-----
189
6.2.1
DEFINITIONS
AND
PROPERTIES
OF
MATRIX
FUNCTIONS
-----
189
6.2.2
COMPUTING
MATRIX
EXPONENTIALS
*
190
6.2.3
TAYLOR
SERIES-BASED
TRUNCATION
ALGORITHM
*
190
6.2.4
A
CAYLEY-HAMILTON
THEOREM-BASED
ALGORITHM
*
192
6.2.5
DIRECT
MATLAB
SOLVER
-----
193
6.2.6
JORDAN
TRANSFORM-BASED
APPROACH
*
195
6.3
MATRIX
LOGARITHMIC
AND
SQUARE
ROOT
FUNCTIONS
*
196
6.3.1
MATRIX
LOGARITHMIC
FUNCTION
-----
196
6.3.2
SQUARE
ROOT
OF
A
MATRIX
-----
198
6.4
MATRIX
TRIGONOMETRIC
FUNCTIONS
-----
199
6.4.1
COMPUTATION
OF
MATRIX
TRIGONOMETRIC
FUNCTIONS
*
199
6.4.2
POWER
SERIES-BASED
TRIGONOMETRIC
FUNCTION
EVALUATION
*
200
6.4.3
ANALYTICAL
EVALUATIONS
OF
MATRIX
TRIGONOMETRIC
FUNCTIONS
*
202
6.5
ARBITRARY
MATRIX
FUNCTIONS
--------
204
6.5.1
NILPOTENT
MATRICES
-----
204
6.5.2
JORDAN
TRANSFORM-BASED
MATRIX
FUNCTION
EVALUATIONS
*
205
6.5.3
USER-DEFINED
MATRIX
FUNCTIONS
*
208
6.6
MATRIX
POWERS
-----
210
6.6.1
MATRIX
POWERS
VIA
JORDAN
TRANSFORM
-----
210
6.6.2
A
MATRIX
POWER
SOLVER
-----
211
6.6.3
MATRIX
POWERS
VIA
THE
Z
TRANSFORM
-----
213
CONTENTS
*
XI
6.6.4
6.7
COMPUTING
-----
214
PROBLEMS
-----
215
7
7.1
7.1.1
7.1.2
7.1.3
7.2
7.2.1
7.2.2
7.2.3
7.2.4
7.3
7.3.1
7.3.2
7.3.3
7.3.4
7.4
7.4.1
7.4.2
7.4.3
7.5
7.5.1
7.5.2
7.5.3
7.5.4
7.5.5
7.6
7.6.1
7.6.2
7.6.3
7.6.4
7.6.5
7.7
LINEAR
ALGEBRA
APPLICATIONS
*
217
LINEAR
EQUATIONS
APPLICATIONS
-----
217
ELECTRIC
NETWORK
ANALYSIS
*
217
ANALYSIS
OF
TRUSS
STRUCTURES
-----
224
BALANCING
CHEMICAL
REACTION
EQUATIONS
-----
224
APPLICATIONS
IN
LINEAR
CONTROL
SYSTEMS
-----
227
CONTROL
SYSTEM
MODEL
CONVERSIONS
-----
227
QUALITATIVE
ANALYSIS
OF
LINEAR
SYSTEMS
*
229
TRANSMISSION
ZEROS
IN
MULTIVARIATE
SYSTEMS
-----
231
DIRECT
SOLUTIONS
OF
LINEAR
DIFFERENTIAL
EQUATIONS
-----
232
INTRODUCTION
TO
DIGITAL
IMAGE
PROCESSING
*
233
IMAGE
INPUT
AND
DISPLAY
-----
234
SINGULAR
VALUE
DECOMPOSITION
APPLICATIONS
*
235
RESIZING
AND
ROTATING
IMAGES
-----
237
IMAGE
ENHANCEMENT
*
239
GRAPH
THEORY
AND
APPLICATIONS
-----
241
ORIENTED
GRAPH
DESCRIPTIONS
-----
242
DIJKSTRA
ALGORITHM
AND
APPLICATIONS
-----
244
SIMPLIFICATION
OF
CONTROL
SYSTEM
BLOCK
DIAGRAMS
*
247
SOLVING
DIFFERENCE
EQUATIONS
-----
251
ANALYTICAL
SOLUTIONS
-----
252
NUMERICAL
SOLUTIONS
OF
LINEAR
TIME-VARYING
DIFFERENCE
EQUATIONS
*
254
LINEAR
TIME-INVARIANT
DIFFERENCE
EQUATIONS
*
255
NUMERICAL
SOLUTIONS
OF
NONLINEAR
DIFFERENCE
EQUATIONS
*
257
MARKOV
CHAIN
SIMULATION
----
258
DATA
FITTING
AND
ANALYSIS
-----
260
LINEAR
REGRESSION
-----
261
POLYNOMIAL
FITTING
----
264
CHEBYSHEV
POLYNOMIALS
*
265
BEZIER
CURVES
-----
267
PRINCIPAL
COMPONENT
ANALYSIS
*
269
EXERCISES
OF
THE
CHAPTER
*
272
BIBLIOGRAPHY
*
279
MATLAB
FUNCTION
INDEX
*
281
INDEX
*
285 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Xue, Dingyu |
| author_GND | (DE-588)1098160967 |
| author_facet | Xue, Dingyu |
| author_role | aut |
| author_sort | Xue, Dingyu |
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| building | Verbundindex |
| bvnumber | BV046775799 |
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| ctrlnum | (OCoLC)1110094940 (DE-599)DNB1190750600 |
| dewey-full | 512.50285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.50285 |
| dewey-search | 512.50285 |
| dewey-sort | 3512.50285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV046775799 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:48:19Z |
| indexdate | 2024-07-10T08:53:29Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110663631 3110663635 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032185105 |
| oclc_num | 1110094940 |
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| owner_facet | DE-703 DE-19 DE-BY-UBM DE-706 DE-20 |
| physical | XI, 289 Seiten Illustrationen, Diagramme 24 cm, 521 g |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter Tsinghua University Press |
| record_format | marc |
| spelling | Xue, Dingyu Verfasser (DE-588)1098160967 aut Linear algebra and matrix computations with MATLAB Dingyü Xue Berlin ; Boston De Gruyter [2020] [Beijing] Tsinghua University Press © 2020 XI, 289 Seiten Illustrationen, Diagramme 24 cm, 521 g txt rdacontent n rdamedia nc rdacarrier MATLAB (DE-588)4329066-8 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s MATLAB (DE-588)4329066-8 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-066699-1 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-066371-6 B:DE-101 application/pdf https://d-nb.info/1190750600/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032185105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xue, Dingyu Linear algebra and matrix computations with MATLAB MATLAB (DE-588)4329066-8 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4035811-2 |
| title | Linear algebra and matrix computations with MATLAB |
| title_auth | Linear algebra and matrix computations with MATLAB |
| title_exact_search | Linear algebra and matrix computations with MATLAB |
| title_exact_search_txtP | Linear algebra and matrix computations with MATLAB |
| title_full | Linear algebra and matrix computations with MATLAB Dingyü Xue |
| title_fullStr | Linear algebra and matrix computations with MATLAB Dingyü Xue |
| title_full_unstemmed | Linear algebra and matrix computations with MATLAB Dingyü Xue |
| title_short | Linear algebra and matrix computations with MATLAB |
| title_sort | linear algebra and matrix computations with matlab |
| topic | MATLAB (DE-588)4329066-8 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | MATLAB Lineare Algebra |
| url | https://d-nb.info/1190750600/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032185105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xuedingyu linearalgebraandmatrixcomputationswithmatlab AT walterdegruytergmbhcokg linearalgebraandmatrixcomputationswithmatlab |
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