Elementary linear algebra with applications: MATLAB, Mathematica and Maplesoft™
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2024]
|
| Schriftenreihe: | De Gruyter Graduate
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| Schlagworte: | |
| Online-Zugang: | https://www.degruyter.com/isbn/9783111331799 Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 671 Seiten Illustrationen, Diagramme 24 cm x 17 cm, 1118 g |
| ISBN: | 9783111331799 3111331792 |
Internformat
MARC
| LEADER | 00000nam a22000008c 4500 | ||
|---|---|---|---|
| 001 | BV049723215 | ||
| 003 | DE-604 | ||
| 005 | 20240712 | ||
| 007 | t | ||
| 008 | 240530s2024 gw a||| |||| 00||| eng d | ||
| 015 | |a 24,N06 |2 dnb | ||
| 016 | 7 | |a 1318173515 |2 DE-101 | |
| 020 | |a 9783111331799 |c Broschur : EUR 74.95 (DE) (freier Preis), EUR 74.95 (AT) (freier Preis) |9 978-3-11-133179-9 | ||
| 020 | |a 3111331792 |9 3-11-133179-2 | ||
| 024 | 3 | |a 9783111331799 | |
| 035 | |a (OCoLC)1443587400 | ||
| 035 | |a (DE-599)DNB1318173515 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-20 |a DE-92 |a DE-29T | ||
| 084 | |a SK 220 |0 (DE-625)143224: |2 rvk | ||
| 084 | |8 1\p |a 510 |2 23sdnb | ||
| 100 | 1 | |a Nakos, George |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elementary linear algebra with applications |b MATLAB, Mathematica and Maplesoft™ |c George Nakos |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2024] | |
| 300 | |a XXVIII, 671 Seiten |b Illustrationen, Diagramme |c 24 cm x 17 cm, 1118 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Graduate | |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 653 | |a Lineare Algebra | ||
| 653 | |a Matrizen | ||
| 653 | |a Lineare Systeme | ||
| 653 | |a Eigenwerte | ||
| 653 | |a Linear algebra | ||
| 653 | |a Matrices | ||
| 653 | |a Linear Systems and Eigenvalues | ||
| 653 | |a TB: Textbook | ||
| 653 | |a Lineare Algebra; Matrizen; Lineare Systeme; Eigenwerte | ||
| 653 | |a Linear algebra; Matrices; Linear Systems and Eigenvalues | ||
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |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 978-3-11-133185-0 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-133195-9 |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783111331799 |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u https://d-nb.info/1318173515/04 |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=035065558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a vlb |d 20240202 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035065558 | |
Datensatz im Suchindex
| _version_ | 1808587425196277760 |
|---|---|
| adam_text |
CONTENTS
PREFACE
-
VII
ACKNOWLEDGMENT
-
XIX
1
LINEAR
SYSTEMS
-
1
1.1
INTRODUCTION
TO
LINEAR
SYSTEMS
-
2
1.1.1
LINEAR
EQUATIONS
-
2
1.1.2
DEFINITION
OF
LINEAR
SYSTEM
-
3
1.1.3
SOLUTION
OF
LINEAR
SYSTEM
-
4
1.1.4
GEOMETRY
OF
SOLUTIONS
IN
TWO
VARIABLES
-
5
1.1.5
BACK-SUBSTITUTION
-
5
1.1.6
INTRODUCTION
TO
GAUSS
ELIMINATION
-
6
1.1.7
GEOMETRY
OF
SOLUTIONS
IN
THREE
VARIABLES
-
8
1.1.8
LINEAR
SYSTEMS
WITH
COMPLEX
NUMBERS
-
9
1.1.9
INTERCHANGES
IN
TERMS
ELIMINATIONS
AND
SCALINGS
-
10
1.2
GAUSS
ELIMINATION
-
16
1.2.1
MATRICES
IN
ECHELON
FORM
-
17
1.2.2
THE
GAUSS
ELIMINATION
ALGORITHM
-
18
1.2.3
SOLUTION
ALGORITHM
FOR
LINEAR
SYSTEMS
-
21
1.2.4
THE
GAUSS-JORDAN
ELIMINATION
ALGORITHM
-
22
1.2.5
EXISTENCE
AND
UNIQUENESS
OF
SOLUTIONS
-
22
1.2.6
HOMOGENEOUS
LINEAR
SYSTEMS
-
24
1.2.7
NUMERICAL
CONSIDERATIONS
-
25
1.3
APPLICATIONS:
ECONOMICS,
CHEMISTRY,
PHYSICS,
ENGINEERING
-
30
1.3.1
ECONOMICS:
THE
DEMAND
FUNCTION,
MARKET
EQUILIBRIA
-
30
1.3.2
CHEMISTRY:
CHEMICAL
SOLUTIONS,
BALANCING
OF
REACTIONS
-
32
1.3.3
PHYSICS
AND
ENGINEERING:
CIRCUITS,
HEAT
CONDUCTION
-
33
1.3.4
TRAFFIC
FLOW
-
35
1.3.5
STATICS
AND
WEIGHT
BALANCING
-
37
1.4
NUMERICAL
SOLUTIONS
OF
LINEAR
SYSTEMS
-
41
1.4.1
COMPUTATIONAL
EFFICIENCY
OF
ROW
REDUCTION
-
41
1.4.2
ITERATIVE
METHODS
-
42
1.4.3
JACOBI
ITERATION
-
42
1.4.4
GAUSS-SEIDEL
ITERATION
-
43
1.4.5
CONVERGENCE
-
44
1.4.6
COMPARISON
OF
ELIMINATION
AND
GAUSS-SEIDEL
ITERATION
-
45
1.4.7
NUMERICAL
CONSIDERATIONS:
ILL-CONDITIONING
AND
PIVOTING
-
46
1.5
MINIPROJECTS
-
49
1.5.1
PSYCHOLOGY:
ANIMAL
INTELLIGENCE
-
49
1.5.2
COUNTING
OPERATIONS
IN
GAUSS
ELIMINATION
-
50
XXII
-
CONTENTS
1.5.3
1.6
1.6.1
1.6.2
1.6.3
ARCHIMEDES
'
CATTLE
PROBLEM
-
51
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
52
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
54
SELECTED
SOLUTIONS
WITH
MATLAB
-
55
SELECTED
SOLUTIONS
WITH
MAPLE
-
56
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
2.1.6
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.3
2.4
2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.6
2.6.1
2.6.2
2.6.3
2.7
2.7.1
2.7.2
2.7.3
2.8
2.9
2.10
2.10.1
2.10.2
2.10.3
VECTORS
-
58
MATRICES
AND
VECTORS
-
59
ADDITION
AND
SCALAR
MULTIPLICATION
-
60
TRANSPOSE,
SYMMETRIC
AND
HERMITIAN
MATRICES
-
62
SPECIAL
SQUARE
MATRICES,
TRACE
-
64
GEOMETRIC
INTERPRETATION
OF
VECTORS
-
65
APPLICATION
OF
LINEAR
COMBINATIONS
-
66
DIGITAL
SIGNALS
-
67
MATRIX
TRANSFORMATIONS
-
72
THE
MATRIX-VECTOR
PRODUCT
-
72
MATRIX
TRANSFORMATIONS
-
74
MATRIX
FORM
OF
LINEAR
SYSTEMS
-
77
RELATION
BETWEEN
THE
SOLUTIONS
OF
AX
=
0
AND
AX
=
B
-
79
THE
SPAN
-
86
LINEAR
INDEPENDENCE
-
93
DOT
PRODUCT,
LINES,
HYPERPLANES
-
100
DOT
PRODUCT
-
100
ORTHOGONAL
PROJECTIONS
-
104
LINES,
PLANES,
AND
HYPERPLANES
-
105
HYPERPLANES
AND
SOLUTIONS
OF
LINEAR
SYSTEMS
-
108
APPLICATION:
COMPUTER
GRAPHICS
-
112
PLANE
MATRIX
TRANSFORMATIONS
-
112
SPACE
MATRIX
TRANSFORMATIONS
-
115
AFFINE
TRANSFORMATIONS
-
116
APPLICATIONS:
AVERAGING,
DYNAMICAL
SYSTEMS
-
123
DATA
SMOOTHING
BY
AVERAGING
-
123
DISCRETE
DYNAMICAL
SYSTEMS
-
125
A
POPULATION
GROWTH
MODEL
-
125
SPECIAL
TOPIC:
TESSELLATIONS
IN
WEATHER
MODELS
-
129
MINIPROJECT:
SPECIAL
AFFINE
TRANSFORMATIONS
-
132
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
133
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
134
SELECTED
SOLUTIONS
WITH
MATLAB
-
135
SELECTED
SOLUTIONS
WITH
MAPLE
-
137
CONTENTS
-
XXIII
3
MATRICES
-
139
3.1
MATRIX
MULTIPLICATION
-
140
3.1.1
ANOTHER
VIEWPOINT
OF
MATRIX
MULTIPLICATION
-
143
3.1.2
POWERS
OF
A
SQUARE
MATRIX
-
144
3.1.3
MATRIX
MULTIPLICATION
WITH
COMPLEX
NUMBERS
-
144
3.1.4
MOTIVATION
FOR
MATRIX
MULTIPLICATION
-
145
3.1.5
COMPUTATIONAL
CONSIDERATIONS
-
146
3.1.6
APPLICATION
TO
COMPUTER
GRAPHICS
-
147
3.1.7
APPLICATION
TO
MANUFACTURING
-
148
3.2
MATRIX
INVERSE
-
154
3.2.1
COMPUTATION
OF
THE
INVERSE
-
155
3.2.2
RELATION
OF
A
-1
TO
SQUARE
SYSTEMS
-
157
3.2.3
PROPERTIES
OF
MATRIX
INVERSION
-
157
3.2.4
MATRIX
POWERS
WITH
NEGATIVE
EXPONENTS
-
158
3.2.5
APPLICATION
TO
STATICS:
STIFFNESS
OF
ELASTIC
BEAM
-
159
3.3
ELEMENTARY
MATRICES
-
163
3.3.1
ELEMENTARY
MATRICES
AND
INVERTIBLE
MATRICES
-
167
3.3.2
THE
MATRIX
INVERSION
ALGORITHM
-
168
3.3.3
CHARACTERIZATION
OF
INVERTIBLE
MATRICES
-
169
3.4
LU
FACTORIZATION
-
173
3.4.1
COMPUTATIONAL
EFFICIENCY
WITH
LU
-
178
3.4.2
LU
WITH
INTERCHANGES
-
178
3.5
BLOCK
AND
SPARSE
MATRICES
-
182
3.5.1
BLOCK
MATRICES
-
182
3.5.2
ADDITION
OF
BLOCK
MATRICES
-
183
3.5.3
MULTIPLICATION
OF
BLOCK
MATRICES
-
184
3.5.4
INVERSION
OF
BLOCK
MATRICES
-
185
3.5.5
SPARSE
MATRICES
-
186
3.6
APPLICATIONS:
LEONTIEF
MODELS,
MARKOV
CHAINS
-
189
3.6.1
STOCHASTIC
MATRICES
-
189
3.6.2
ECONOMICS:
LEONTIEF
INPUT-OUTPUT
MODELS
-
189
3.6.3
PROBABILITY
MATRICES
AND
MARKOV
PROCESSES
-
193
3.7
GRAPH
THEORY
-
198
3.7.1
GRAPHS
-
198
3.7.2
SOCIOLOGY
AND
PSYCHOLOGY:
DOMINANCE
GRAPHS
-
201
3.8
MINIPROJECTS
-
206
3.8.1
CRYPTOLOGY:
THE
HILL
CIPHER
-
206
3.8.2
TRANSITION
OF
PROBABILITIES
-
207
3.8.3
DIGRAPH
WALKS
-
208
3.8.4
A
THEORETICAL
PROBLEM
-
208
3.9
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
209
3.9.1
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
210
XXIV
-
CONTENTS
3.9.2
3.9.3
SELECTED
SOLUTIONS
WITH
MATLAB
-
211
SELECTED
SOLUTIONS
WITH
MAPLE
-
213
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.3
4.3.1
4.3.2
4.3.3
4.4
4.4.1
4.4.2
4.5
4.6
4.6.1
4.6.2
4.6.3
4.6.4
4.7
4.7.1
4.7.2
4.7.3
4.7.4
4.8
4.9
4.9.1
4.9.2
4.9.3
VECTOR
SPACES
-
215
VECTOR
SPACE
-
216
DEFINITION
AND
PROPERTIES
-
216
EXAMPLES
OF
VECTOR
SPACES
-
218
SUBSPACES
-
220
COMPLEX
VECTOR
SPACES
-
221
SPAN,
LINEAR
INDEPENDENCE
-
225
SPAN
-
225
LINEAR
DEPENDENCE
-
228
LINEAR
INDEPENDENCE
-
229
LINEAR
DEPENDENCE
FOR
SEQUENCES
-
231
BASIS,
DIMENSION
-
235
BASIS
OF
A
VECTOR
SPACE
-
235
DIMENSION
-
239
ORDERED
BASES
-
243
COORDINATES,
CHANGE
OF
BASIS
-
247
COORDINATE
VECTORS
-
247
CHANGE
OF
BASIS
-
250
NULL
SPACE
-
256
COLUMN
SPACE,
ROW
SPACE,
RANK
-
260
THE
COLUMN
SPACE
-
260
THE
ROW
SPACE
-
263
RANK
-
265
RANK
AND
LINEAR
SYSTEMS
-
266
APPLICATION
TO
CODING
THEORY
-
271
VECTOR
SPACES
OVER
Z
2
-
272
THE
HAMMING
(7,
4)-CODE
-
274
ENCODING
AND
DECODING
-
276
OTHER
TYPES
OF
CODES
-
277
MINIPROJECTS
-
279
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
283
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
284
SELECTED
SOLUTIONS
WITH
MATLAB
-
286
SELECTED
SOLUTIONS
WITH
MAPLE
-
287
5
5.1
5.1.1
5.2
LINEAR
TRANSFORMATIONS
-
289
LINEAR
TRANSFORMATIONS
-
290
EVALUATION
OF
LINEAR
TRANSFORMATION
FROM
A
BASIS
-
294
KERNEL
AND
RANGE
-
297
CONTENTS
-
XXV
5.2.1
5.3
5.3.1
5.3.2
5.4
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.5
5.5.1
5.6
5.6.1
5.7
5.7.1
5.7.2
5.7.3
ISOMORPHISMS
-
300
MATRIX
OF
LINEAR
TRANSFORMATION
-
307
CHANGE
OF
BASIS
AND
THE
MATRIX
OF
A
LINEAR
TRANSFORMATION
-
310
PROOF
OF
DIMENSION
THEOREM
-
312
THE
ALGEBRA
OF
LINEAR
TRANSFORMATIONS
-
315
SUMS
AND
SCALAR
PRODUCTS
-
315
COMPOSITION
OF
LINEAR
TRANSFORMATIONS
-
316
PROJECTIONS
-
317
LINEAR
TRANSFORMATION
AND
MATRIX
OPERATIONS
-
318
INVERTIBLE
LINEAR
TRANSFORMATIONS
-
318
SPECIAL
TOPIC:
FRACTALS
-
322
FRACTALS
-
322
MINIPROJECT
-
324
ANOTHER
FRACTAL
-
324
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
325
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
327
SELECTED
SOLUTIONS
WITH
MATLAB
-
328
SELECTED
SOLUTIONS
WITH
MAPLE
-
330
6
6.1
6.1.1
6.1.2
6.1.3
6.2
6.2.1
6.2.2
6.3
6.3.1
6.3.2
6.4
6.4.1
6.4.2
6.5
6.5.1
6.5.2
6.6
6.6.1
6.6.2
6.6.3
6.6.4
6.7
DETERMINANTS
-
333
DETERMINANTS:
BASIC
CONCEPTS
-
334
COFACTOR
EXPANSION
-
334
GEOMETRIC
PROPERTY
OF
THE
DETERMINANT
-
338
THE
SARRUS
SCHEME
FOR
3
X
3
DETERMINANTS
-
339
PROPERTIES
OF
DETERMINANTS
-
343
ELEMENTARY
OPERATIONS
AND
DETERMINANTS
-
343
MATRIX
OPERATIONS
AND
DETERMINANTS
-
347
THE
ADJOINT;
CRAMER
'
S
RULE
-
354
ADJOINT
AND
INVERSE
-
354
CRAMER
'
S
RULE
-
356
DETERMINANTS
WITH
PERMUTATIONS
-
359
PERMUTATIONS
-
359
COMPUTATIONAL
CONSIDERATION
-
363
APPLICATIONS:
GEOMETRY,
POLYNOMIAL
SYSTEMS
-
365
EQUATIONS
OF
GEOMETRIC
OBJECTS
-
366
ELIMINATION
THEORY,
RESULTANTS,
AND
POLYNOMIAL
SYSTEMS
-
368
SPECIAL
TOPIC:
IMAGE
RECOGNITION
-
374
INTRODUCTION
TO
PROJECTIVE
GEOMETRY
-
374
PROJECTIVE
TRANSFORMATIONS
-
377
PROJECTIVE
INVARIANTS
-
378
THE
OBJECT-IMAGE
EQUATIONS
-
380
MINIPROJECTS
-
381
XXVI
-
CONTENTS
6.7.1
VANDERMONDE
DETERMINANTS
-
381
6.7.2
BEZOUT
RESULTANT
-
383
6.8
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
385
6.8.1
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
386
6.8.2
SELECTED
SOLUTIONS
WITH
MATLAB
-
388
6.8.3
SELECTED
SOLUTIONS
WITH
MAPLE
-
390
7 EIGENVALUES
-
392
7.1
EIGENVALUES
AND
EIGENVECTORS
-
393
7.1.1
COMPUTATION
OF
EIGENVALUES
AND
EIGENVECTORS
-
395
7.1.2
EIGENVALUES
OF
LINEAR
OPERATORS
-
400
7.1.3
NUMERICAL
NOTE
-
401
7.2
DIAGONALIZATION
-
405
7.2.1
DIAGONALIZATION
OF
MATRICES
-
406
7.2.2
POWERS
OF
DIAGONALIZABLE
MATRICES
-
410
7.2.3
AN
IMPORTANT
CHANGE
OF
VARIABLES
-
410
7.3
APPLICATIONS:
DISCRETE
DYNAMICAL
SYSTEMS
-
414
7.3.1
BASIC
CONCEPTS
-
414
7.3.2
LONG-TERM
BEHAVIOR
OF
DYNAMICAL
SYSTEMS
-
416
7.3.3
UNCOUPLING
DYNAMICAL
SYSTEMS
-
422
7.4
APPLICATIONS:
DYNAMICAL
SYSTEMS
(2)
AND
MARKOV
CHAINS
-
424
7.4.1
DYNAMICAL
SYSTEMS
WITH
COMPLEX
EIGENVALUES
-
424
7.4.2
APPLICATION
TO
A
POPULATION
GROWTH
PROBLEM
-
426
7.4.3
MARKOV
CHAINS
AND
STOCHASTIC
MATRICES
-
428
7.4.4
LIMITS
OF
STOCHASTIC
MATRICES
-
429
7.5
SPECIAL
TOPIC:
THE
PAGERANK
ALGORITHM
OF
GOOGLE
-
434
7.6
APPROXIMATIONS
OF
EIGENVALUES
-
436
7.6.1
THE
POWER
METHOD
-
437
7.6.2
RAYLEIGH
QUOTIENTS
(THE
RAYLEIGH-RITZ
METHOD)
-
440
7.6.3
ORIGIN
SHIFTS
-
442
7.6.4
INVERSE
POWER
METHOD
-
442
7.6.5
SHIFTED
INVERSE
POWER
METHOD
-
444
7.6.6
APPLICATION
TO
ROOTS
OF
POLYNOMIALS
-
445
7.7
MINIPROJECTS
-
448
7.7.1
THE
CAYLEY-HAMILTON
THEOREM
-
448
7.7.2
GERSCHGORIN
CIRCLES
-
450
7.7.3
TRANSITION
OF
PROBABILITIES
(PART
2)
-
451
7.8
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
452
7.8.1
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
454
7.8.2
SELECTED
SOLUTIONS
WITH
MATLAB
-
455
7.8.3
SELECTED
SOLUTIONS
WITH
MAPLE
-
457
CONTENTS
-
XXVII
8
ORTHOGONALITY
AND
LEAST
SQUARES
-
459
8.1
ORTHOGONAL
SETS
AND
MATRICES
-
460
8.1.1
ORTHOGONAL
SETS
-
460
8.1.2
ORTHONORMAL
SETS
-
463
8.1.3
ORTHOGONAL
MATRICES
-
465
8.1.4
WHAT
MAKES
ORTHOGONAL
MATRICES
IMPORTANT
-
467
8.2
THE
GRAM-SCHMIDT
PROCESS
-
471
8.2.1
ORTHOGONAL
COMPLEMENTS
-
472
8.2.2
ORTHOGONAL
PROJECTIONS
AND
BEST
APPROXIMATION
-
474
8.2.3
THE
GRAM-SCHMIDT
PROCESS
-
478
8.2.4
DISTANCE
AND
ANGLE
FROM
VECTOR
TO
SUBSPACE
-
481
8.3
THE
QR
FACTORIZATION
-
486
8.3.1
THE
QR
METHOD
FOR
EIGENVALUES
-
488
8.3.2
HOUSEHOLDER
TRANSFORMATIONS
AND
QR
-
489
8.4
LEAST
SQUARES
-
494
8.4.1
A
LEAST
SQUARES
PROBLEM
-
495
8.4.2
SOLUTION
OF
THE
LEAST
SQUARES
PROBLEM
-
496
8.4.3
LEAST
SQUARES
WITH
QR
FACTORIZATION
-
501
8.5
INNER
PRODUCT
SPACES
-
506
8.5.1
DEFINITION
OF
INNER
PRODUCT
-
506
8.5.2
EXAMPLES
OF
INNER
PRODUCTS
-
507
8.5.3
LENGTH
AND
ORTHOGONALITY
-
512
8.5.4
BASIC
IDENTITIES
AND
INEQUALITIES
-
514
8.5.5
THE
GRAM-SCHMIDT
PROCESS
-
517
8.6
COMPLEX
INNER
PRODUCTS;
UNITARY
MATRICES
-
522
8.6.1
DEFINITION
AND
EXAMPLES
-
522
8.6.2
UNITARY
MATRICES
-
524
8.7
POLYNOMIAL
AND
CONTINUOUS
LEAST
SQUARES
-
529
8.7.1
POLYNOMIAL
LEAST
SQUARES
-
529
8.7.2
CONTINUOUS
LEAST
SQUARES
(REQUIRES
CALCULUS)
-
533
8.8
SPECIAL
TOPIC:
THE
NFL
RATING
OF
QUARTERBACKS
-
537
8.9
MINIPROJECTS
-
540
8.9.1
THE
PAULI
SPIN
AND
DIRAC
MATRICES
-
540
8.9.2
RIGID
MOTIONS
IN
R"
-
541
8.9.3
VOLUME
OF
THE
PARALLELEPIPED
AND
THE
GRAM
DETERMINANT
-
543
8.10
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
543
8.10.1
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
544
8.10.2
SELECTED
SOLUTIONS
WITH
MATLAB
-
546
8.10.3
SELECTED
SOLUTIONS
WITH
MAPLE
-
548
9
QUADRATIC
FORMS,
SVD,
WAVELETS
-
551
9.1
ORTHOGONALIZATION
OF
SYMMETRIC
MATRICES
-
553
XXVIII
-
CONTENTS
9.1.1
9.2
9.2.1
9.2.2
9.2.3
9.3
9.3.1
9.3.2
9.3.3
9.3.4
9.4
9.5
9.6
9.7
9.7.1
9.7.2
9.8
9.8.1
9.8.2
9.8.3
PROOF
OF
SCHUR
'
S
DECOMPOSITION
THEOREM
AND
EXAMPLE
-
557
QUADRATIC
FORMS
AND
CONIC
SECTIONS
-
561
DIAGONALIZATION
OF
QUADRATIC
FORMS
-
562
APPLICATIONS
OF
QUADRATIC
FORMS
TO
GEOMETRY
-
563
POSITIVE
AND
NEGATIVE
DEFINITE
QUADRATIC
FORMS
-
567
THE
SINGULAR
VALUE
DECOMPOSITION
(SVD)
-
569
SINGULAR
VALUES;
FINDING
V,
Z,
AND
U
-
570
PSEUDOINVERSE
-
576
SVD
AND
LEAST
SQUARES
-
577
THE
POLAR
DECOMPOSITION
OF
A
SQUARE
MATRIX
-
579
SPECIAL
TOPIC:
SVD
AND
IMAGE
COMPRESSION
-
582
FOURIER
SERIES
AND
POLYNOMIALS
-
584
APPLICATION
TO
WAVELETS
-
588
MINIPROJECTS
-
593
WAVELETS
-
593
AN
IMAGE
COMPRESSION
PROJECT
GENERATED
BY
CHATGPT
-
595
TECHNOLOGY-AIDED
PROBLEMS
AND
ANSWERS
-
596
SELECTED
SOLUTIONS
WITH
MATHEMATICA
-
598
SELECTED
SOLUTIONS
WITH
MATLAB
-
599
SELECTED
SOLUTIONS
WITH
MAPLE
-
600
A
A.1
A.2
INTRODUCTION
TO
COMPLEX
NUMBERS
-
603
ARITHMETIC
WITH
COMPLEX
NUMBERS
-
603
GEOMETRIC
INTERPRETATION
OF
COMPLEX
NUMBERS
-
604
B
UNIQUENESS
OF
RREF
-
607
ANSWERS
TO
SELECTED
EXERCISES
-
609
BIBLIOGRAPHY
-
659
INDEX
OF
APPLICATIONS
-
661
INDEX
-
663 |
| any_adam_object | 1 |
| author | Nakos, George |
| author_facet | Nakos, George |
| author_role | aut |
| author_sort | Nakos, George |
| author_variant | g n gn |
| building | Verbundindex |
| bvnumber | BV049723215 |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)1443587400 (DE-599)DNB1318173515 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV049723215 |
| illustrated | Illustrated |
| indexdate | 2024-08-28T00:02:55Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111331799 3111331792 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035065558 |
| oclc_num | 1443587400 |
| open_access_boolean | |
| owner | DE-20 DE-92 DE-29T |
| owner_facet | DE-20 DE-92 DE-29T |
| physical | XXVIII, 671 Seiten Illustrationen, Diagramme 24 cm x 17 cm, 1118 g |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spelling | Nakos, George Verfasser aut Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ George Nakos Berlin ; Boston De Gruyter [2024] XXVIII, 671 Seiten Illustrationen, Diagramme 24 cm x 17 cm, 1118 g txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Lineare Algebra Matrizen Lineare Systeme Eigenwerte Linear algebra Matrices Linear Systems and Eigenvalues TB: Textbook Lineare Algebra; Matrizen; Lineare Systeme; Eigenwerte Linear algebra; Matrices; Linear Systems and Eigenvalues Lineare Algebra (DE-588)4035811-2 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-133185-0 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-133195-9 X:MVB https://www.degruyter.com/isbn/9783111331799 B:DE-101 application/pdf https://d-nb.info/1318173515/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035065558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20240202 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Nakos, George Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4035811-2 |
| title | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ |
| title_auth | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ |
| title_exact_search | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ |
| title_full | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ George Nakos |
| title_fullStr | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ George Nakos |
| title_full_unstemmed | Elementary linear algebra with applications MATLAB, Mathematica and Maplesoft™ George Nakos |
| title_short | Elementary linear algebra with applications |
| title_sort | elementary linear algebra with applications matlab mathematica and maplesoft™ |
| title_sub | MATLAB, Mathematica and Maplesoft™ |
| topic | Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra |
| url | https://www.degruyter.com/isbn/9783111331799 https://d-nb.info/1318173515/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035065558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nakosgeorge elementarylinearalgebrawithapplicationsmatlabmathematicaandmaplesoft AT walterdegruytergmbhcokg elementarylinearalgebrawithapplicationsmatlabmathematicaandmaplesoft |
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