kreyzig ch 08 linear algebra
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Matrix Eigenvalue Problems
TF2101
Matematika Rekayasa Sistem
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Matrix Eigenvalue Problems
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
22
25A
2
1
2
1
22
25
x
x
x
xAx
221
121
22
25
xxx
xxx
0)2(2
02)5(
21
21
xx
xx
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Pages 335-336a
Continued
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Pages 339-340a
Continued
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Continued
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Pages 339-340c
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 346 (3)
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Eigenbases, Diagonalization, Quadratic Forms
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Example
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 352
>> [V,E] =eig(A)V = -0.3015 0.4364 -0.3015 0.3015 0.2182 0.9045 -0.9045 0.8729 -0.3015 E = -4.0000 0 0 0 -0.0000 0 0 0 3.0000
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Quadratic Forms. Transformation to Principal Axes
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 353 (2)
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 353 (3)
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 354 (1)
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 354 (2a)
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Complex Matrices and FormsThe three classes of real matrices have complex counterparts that are of practical interest in certain applications, mainly because of their spectra, for instance in quantum mechanics. To define these classes, we need the following standard.
ii
i
i
ii
i
ii
521
643,
526
143,
526
143 TAAA
Example if then and
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
i
i
ii
ii
i
i
2
13
2
1
32
1
2
1
,2
23,
731
314CBA
Example Hermitian Skew-Hermitian unitary
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
i
i
ii
ii
i
i
2
13
2
1
32
1
2
1
,2
23,
731
314CBA
Example Hermitian Skew-Hermitian unitary
iii
iii
32
1,3
2
101:
2,4082:
2,901811:
2
2
2
C
B
ACharacteristic equation Eigenvalues
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
Page 363a
Continued
Advanced Engineering Mathematics by Erwin KreyszigCopyright 2007 John Wiley & Sons, Inc. All rights reserved.
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