Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A* ? The singular values of A and A* are exactly the same, including multiplicities. The non-zero singular values of A and A* are exactly the same, including multiplicities, but if O is a singular value of one matrix, it is not necessarily a singular value of the other.
Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A* ? The singular values of A and A* are exactly the same, including multiplicities. The non-zero singular values of A and A* are exactly the same, including multiplicities, but if O is a singular value of one matrix, it is not necessarily a singular value of the other.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 41EQ:
In general, it is difficult to show that two matrices are similar. However, if two similar matrices...
Related questions
Question
![Suppose we are given
A E Mmxn(C).
How do the singular values of
A
relate to those of its adjoint,
A* ?
The singular values of
A
and
A*
are exactly the same, including multiplicities.
The non-zero singular values of
A
and
A*
are exactly the same, including multiplicities, but if O is a singular value of
one matrix, it is not necessarily a singular value of the other.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2F6567c197-9bde-488e-98fe-716345b47309%2F0oamz9b_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose we are given
A E Mmxn(C).
How do the singular values of
A
relate to those of its adjoint,
A* ?
The singular values of
A
and
A*
are exactly the same, including multiplicities.
The non-zero singular values of
A
and
A*
are exactly the same, including multiplicities, but if O is a singular value of
one matrix, it is not necessarily a singular value of the other.
![The matrices
A
and
A*
do not necessarily have any relationship between their singular values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2F6567c197-9bde-488e-98fe-716345b47309%2F4bi4cz_processed.png&w=3840&q=75)
Transcribed Image Text:The matrices
A
and
A*
do not necessarily have any relationship between their singular values.
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