6.7. Which of the following pairs of matrices are unitarily equivalent: 1 0 0 1 a) ( and 1 1 1/2 1/2 0 1 b) 1 and

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1 0
c)
-1
and
-1
0 0
1
0 0
1
1
0 0
d)
-1
and
-i
1
i
1
1
1
0 0
e)
2
2
and
2
3
3
Hint: It is easy to eliminate matrices that are not unitarily equivalent: remember,
that unitarily equivalent matrices are similar, and trace, determinant and eigenval-
ues of similar matrices coincide.
Also, the previous problem helps in eliminating non unitarily equivalent matri-
ces.
Finally, a matrix is unitarily equivalent to a diagonal one if and only if it has
an orthogonal basis of eigenvectors.
Transcribed Image Text:1 0 c) -1 and -1 0 0 1 0 0 1 1 0 0 d) -1 and -i 1 i 1 1 1 0 0 e) 2 2 and 2 3 3 Hint: It is easy to eliminate matrices that are not unitarily equivalent: remember, that unitarily equivalent matrices are similar, and trace, determinant and eigenval- ues of similar matrices coincide. Also, the previous problem helps in eliminating non unitarily equivalent matri- ces. Finally, a matrix is unitarily equivalent to a diagonal one if and only if it has an orthogonal basis of eigenvectors.
6.7. Which of the following pairs of matrices are unitarily equivalent:
0 1
1
a)
:)
and
1
1
0 1
b)
1/2 ):
1/2 0
and
1
Transcribed Image Text:6.7. Which of the following pairs of matrices are unitarily equivalent: 0 1 1 a) :) and 1 1 0 1 b) 1/2 ): 1/2 0 and 1
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