Compare two symmetric positive semidefinite matrices’ eigenvalues
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A Positive definite diagonal matrix $W=text{diag}{w_1,w_2,...,w_n}$ and a symmetric positive semi definite matrix $A$ with eigenvalues in ascending order $λ_1leqλ_2leqcdotsleqλ_kleqcdotsλ_n:$ are given.
Prove eigevalue of two matrices satisfy $$λ_k(Wcdot A)geq w_{min}cdotλ_k(A)$$
enter image description here
matrices
edited Nov 22 at 13:37
Yadati Kiran
1,352418
asked Nov 22 at 13:27
Wei
11
add a comment |
up vote
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down vote
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A Positive definite diagonal matrix $W=text{diag}{w_1,w_2,...,w_n}$ and a symmetric positive semi definite matrix $A$ with eigenvalues in ascending order $λ_1leqλ_2leqcdotsleqλ_kleqcdotsλ_n:$ are given.
Prove eigevalue of two matrices satisfy $$λ_k(Wcdot A)geq w_{min}cdotλ_k(A)$$
enter image description here
matrices
edited Nov 22 at 13:37
Yadati Kiran
1,352418
asked Nov 22 at 13:27
Wei
11
Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
A Positive definite diagonal matrix $W=text{diag}{w_1,w_2,...,w_n}$ and a symmetric positive semi definite matrix $A$ with eigenvalues in ascending order $λ_1leqλ_2leqcdotsleqλ_kleqcdotsλ_n:$ are given.
Prove eigevalue of two matrices satisfy $$λ_k(Wcdot A)geq w_{min}cdotλ_k(A)$$
enter image description here
matrices
edited Nov 22 at 13:37
Yadati Kiran
1,352418
asked Nov 22 at 13:27
Wei
11
A Positive definite diagonal matrix $W=text{diag}{w_1,w_2,...,w_n}$ and a symmetric positive semi definite matrix $A$ with eigenvalues in ascending order $λ_1leqλ_2leqcdotsleqλ_kleqcdotsλ_n:$ are given.
Prove eigevalue of two matrices satisfy $$λ_k(Wcdot A)geq w_{min}cdotλ_k(A)$$
enter image description here
matrices
matrices
edited Nov 22 at 13:37
Yadati Kiran
1,352418
asked Nov 22 at 13:27
Wei
11
edited Nov 22 at 13:37
Yadati Kiran
1,352418
asked Nov 22 at 13:27
Wei
11
edited Nov 22 at 13:37
Yadati Kiran
1,352418
edited Nov 22 at 13:37
Yadati Kiran
1,352418
edited Nov 22 at 13:37
Yadati Kiran
1,352418
1,352418
asked Nov 22 at 13:27
Wei
11
asked Nov 22 at 13:27
Wei
11
asked Nov 22 at 13:27
Wei
11
11
Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46
add a comment |
Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46
Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46
add a comment |
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Please add your attempts in your post, or you would get downvotes, and the post would highly likely be closed.
– xbh
Nov 22 at 13:31
Sorry，I don't know how to do this problem. I just want to get the eigenvalues range of matrix WA.
– Wei
Nov 22 at 14:46