Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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,...
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95c8cb38-7b7e-4922-9086-588b58242ff8%2Ff6bb342e-9a2a-470f-9f2d-62e305c42f8e%2Fagb91qc_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95c8cb38-7b7e-4922-9086-588b58242ff8%2Ff6bb342e-9a2a-470f-9f2d-62e305c42f8e%2Fxwklq1a_processed.png&w=3840&q=75)
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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