Notation for eigenvalues
$begingroup$
Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.
Is there a simpler, more accepted way to write this?
notation eigenvalues-eigenvectors
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
$endgroup$
add a comment |
$begingroup$
Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.
Is there a simpler, more accepted way to write this?
notation eigenvalues-eigenvectors
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
$endgroup$
1
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
1
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07
add a comment |
$begingroup$
Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.
Is there a simpler, more accepted way to write this?
notation eigenvalues-eigenvectors
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
$endgroup$
Is there a specific notation for eigenvalues? specifically, I'd like to write:
$$mequiv text{smallest eigenvaue of }H$$
I've seen some sources write this as: $Hsucceq mI$, where "$succeq0$" means the matrix is semi positive definite, but it seems a bit convoluted.
Is there a simpler, more accepted way to write this?
notation eigenvalues-eigenvectors
notation eigenvalues-eigenvectors
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
asked Dec 26 '15 at 15:01
nbubisnbubis
27.3k552110
27.3k552110
1
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
1
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07
add a comment |
1
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
1
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07
1
1
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
1
1
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."
Then, you just say $lambda_1$.
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
$endgroup$
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
add a comment |
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%2f1589568%2fnotation-for-eigenvalues%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."
Then, you just say $lambda_1$.
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
$endgroup$
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
add a comment |
$begingroup$
Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."
Then, you just say $lambda_1$.
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
$endgroup$
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
add a comment |
$begingroup$
Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."
Then, you just say $lambda_1$.
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
$endgroup$
Normally one says something like "Let $lambda_1, ldots, lambda_n$ be the eigenvalues of $H$ in non-decreasing order." or "Let $lambda_1 leq ldotsleq lambda_n$ be the eigenvalues of $H$."
Then, you just say $lambda_1$.
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
answered Dec 26 '15 at 15:04
BatmanBatman
16.5k11735
16.5k11735
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
add a comment |
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
I take this as "no".
$endgroup$
– nbubis
Dec 29 '15 at 10:08
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
$begingroup$
Pretty much. Just stating the fact in words is a good way to go as well ("Let $m$ be the smallest eigenvalue of $H$) if you only need the smallest eigenvalue, as suggested in the comments to the original question
$endgroup$
– Batman
Dec 29 '15 at 15:46
add a comment |
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.
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%2f1589568%2fnotation-for-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
1
$begingroup$
I don't believe there's a standard notation for the smallest eigenvalue. I assume you mean smallest in absolute value? And it wouldn't necessarily be unique so that's also problematic.
$endgroup$
– Gregory Grant
Dec 26 '15 at 15:03
1
$begingroup$
What's wrong with saying something like "let $m$ be the smallest eigenvalue of $H$"? Provided that this makes sense, of course (see Gregory's comment above)...
$endgroup$
– A.P.
Dec 26 '15 at 15:07