Compare two symmetric positive semidefinite matrices’ eigenvalues
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
1,702519
asked Nov 22 at 13:27
Wei
11
add a comment |
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
1,702519
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 |
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
1,702519
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
1,702519
asked Nov 22 at 13:27
Wei
11
edited Nov 22 at 13:37
Yadati Kiran
1,702519
asked Nov 22 at 13:27
Wei
11
edited Nov 22 at 13:37
Yadati Kiran
1,702519
edited Nov 22 at 13:37
Yadati Kiran
1,702519
edited Nov 22 at 13:37
Yadati Kiran
1,702519
1,702519
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 |
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009131%2fcompare-two-symmetric-positive-semidefinite-matrices-eigenvalues%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3009131%2fcompare-two-symmetric-positive-semidefinite-matrices-eigenvalues%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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