Kreyzig ch 08 linear algebra

1. Matrix Eigenvalue Problems TF2101 Matematika Rekayasa Sistem

12. − 5 2  A=  2 − 2    x   − 5 2  x1     = λ  1  Ax =    x   2 − 2  x 2   2 − 5 x1 + 2 x 2 = λx1 2 x1 − 2 x 2 = λx 2 (−5 − λ ) x1 + 2 x 2 = 0 2 x1 + (−2 − λ ) x 2 = 0 Advanced Engineering Mathematics by Erwin Kreyszig Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.

30. 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 Kreyszig Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.

37. Complex Matrices and Forms The 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. Example if then and 6   3 + 4i 1 − i   3 − 4i 1 + i   3 − 4i T , A =  , A =  A=  6   6   1 + i 2 + 5i   2 − 5i  2 + 5i      Advanced Engineering Mathematics by Erwin Kreyszig Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.

38. unitary 1   1 i 3  1 − 3i  2 + i  4  3i 2  , B =  , C =  2 A= 1 + 3i − 2 + i − i  1  7  1 3     i   2  2 Example Hermitian Skew-Hermitian Advanced Engineering Mathematics by Erwin Kreyszig Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.

39. unitary 1   1 3  i 1 − 3i  2 + i  4  3i 2 2  , B =  A= 1 + 3i   − 2 + i − i , C =  1  1  7      3 i   2  2 Example Hermitian Skew-Hermitian Characteristic equation A : λ2 − 11λ + 18 = 0 B : λ2 − 2iλ + 8 = 0 C: λ 2 − iλ − 1 = 0 Eigenvalues 1 2 ( 9, 2 4i, − 2i 1 3+i , − 3+i 2 ) ( ) Advanced Engineering Mathematics by Erwin Kreyszig Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.

Kreyzig ch 08 linear algebra

More Related Content

Similar to Kreyzig ch 08 linear algebra (20)

Kreyzig ch 08 linear algebra