Identifying the First Eigenvector
up vote
1
down vote
favorite
If I'm using a programming language which uses a covariance matrix to find the eigenvectors and eigenvalues, how do you know which is the first eigenvector of the covariance matrix?
For example, suppose the following eigenvalues are returned,
0.1017 0 0 0
0 4.1704 0 0
0 0 7.2938 0
0 0 0 23.8721
and suppose the corresponding eigenvectors are
.9032 .28394 .3242 -.453
.343 -.23423 -.234234 .2342
-.3423 .76940 .2938 .7584
.76859 .9873 .3242 -.8721
I thought I read somewhere that it's convention to make the first eigenvalue be the one with the largest value. Is this correct? If so, then because the fourth column has the largest corresponding eigenvalue, then the fourth column would actually be the first egienvector? Or do you just take the first column to be the first eigenvector?
eigenvalues-eigenvectors
asked Nov 26 at 7:07
user6259845
42029
add a comment |
up vote
1
down vote
favorite
If I'm using a programming language which uses a covariance matrix to find the eigenvectors and eigenvalues, how do you know which is the first eigenvector of the covariance matrix?
For example, suppose the following eigenvalues are returned,
0.1017 0 0 0
0 4.1704 0 0
0 0 7.2938 0
0 0 0 23.8721
and suppose the corresponding eigenvectors are
.9032 .28394 .3242 -.453
.343 -.23423 -.234234 .2342
-.3423 .76940 .2938 .7584
.76859 .9873 .3242 -.8721
I thought I read somewhere that it's convention to make the first eigenvalue be the one with the largest value. Is this correct? If so, then because the fourth column has the largest corresponding eigenvalue, then the fourth column would actually be the first egienvector? Or do you just take the first column to be the first eigenvector?
eigenvalues-eigenvectors
asked Nov 26 at 7:07
user6259845
42029
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
If I'm using a programming language which uses a covariance matrix to find the eigenvectors and eigenvalues, how do you know which is the first eigenvector of the covariance matrix?
For example, suppose the following eigenvalues are returned,
0.1017 0 0 0
0 4.1704 0 0
0 0 7.2938 0
0 0 0 23.8721
and suppose the corresponding eigenvectors are
.9032 .28394 .3242 -.453
.343 -.23423 -.234234 .2342
-.3423 .76940 .2938 .7584
.76859 .9873 .3242 -.8721
I thought I read somewhere that it's convention to make the first eigenvalue be the one with the largest value. Is this correct? If so, then because the fourth column has the largest corresponding eigenvalue, then the fourth column would actually be the first egienvector? Or do you just take the first column to be the first eigenvector?
eigenvalues-eigenvectors
asked Nov 26 at 7:07
user6259845
42029
If I'm using a programming language which uses a covariance matrix to find the eigenvectors and eigenvalues, how do you know which is the first eigenvector of the covariance matrix?
For example, suppose the following eigenvalues are returned,
0.1017 0 0 0
0 4.1704 0 0
0 0 7.2938 0
0 0 0 23.8721
and suppose the corresponding eigenvectors are
.9032 .28394 .3242 -.453
.343 -.23423 -.234234 .2342
-.3423 .76940 .2938 .7584
.76859 .9873 .3242 -.8721
I thought I read somewhere that it's convention to make the first eigenvalue be the one with the largest value. Is this correct? If so, then because the fourth column has the largest corresponding eigenvalue, then the fourth column would actually be the first egienvector? Or do you just take the first column to be the first eigenvector?
eigenvalues-eigenvectors
eigenvalues-eigenvectors
asked Nov 26 at 7:07
user6259845
42029
asked Nov 26 at 7:07
user6259845
42029
asked Nov 26 at 7:07
user6259845
42029
asked Nov 26 at 7:07
user6259845
42029
asked Nov 26 at 7:07
user6259845
42029
42029
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
When writing on paper, yes, you may arrange the eigenvalues at a decreasing order. For Matlab, though, the eigenvectors correspond to the "coordinate arrangement" yielded for the eigenvalues by the matrix of them.
answered Nov 26 at 7:11
Rebellos
13.4k21142
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
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',
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%2f3013968%2fidentifying-the-first-eigenvector%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
up vote
1
down vote
accepted
When writing on paper, yes, you may arrange the eigenvalues at a decreasing order. For Matlab, though, the eigenvectors correspond to the "coordinate arrangement" yielded for the eigenvalues by the matrix of them.
answered Nov 26 at 7:11
Rebellos
13.4k21142
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
add a comment |
up vote
1
down vote
accepted
When writing on paper, yes, you may arrange the eigenvalues at a decreasing order. For Matlab, though, the eigenvectors correspond to the "coordinate arrangement" yielded for the eigenvalues by the matrix of them.
answered Nov 26 at 7:11
Rebellos
13.4k21142
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
When writing on paper, yes, you may arrange the eigenvalues at a decreasing order. For Matlab, though, the eigenvectors correspond to the "coordinate arrangement" yielded for the eigenvalues by the matrix of them.
answered Nov 26 at 7:11
Rebellos
13.4k21142
When writing on paper, yes, you may arrange the eigenvalues at a decreasing order. For Matlab, though, the eigenvectors correspond to the "coordinate arrangement" yielded for the eigenvalues by the matrix of them.
answered Nov 26 at 7:11
Rebellos
13.4k21142
answered Nov 26 at 7:11
Rebellos
13.4k21142
answered Nov 26 at 7:11
Rebellos
13.4k21142
answered Nov 26 at 7:11
Rebellos
13.4k21142
13.4k21142
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
add a comment |
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
So to be clear, since I'm using Matlab, the first eignvector is just the first column, regardless of the corresponding eigenvalues?
– user6259845
Nov 26 at 7:17
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
No, the first eigenvalue corresponds to the first eigenvector per Matlab order and so on. What I said, is that eigenvalues and eigenvectors aren't differently ordered and/or decrrasinglly ordered. Eigenvalues and Eigenvectors MUST come in corresponding pairs to make sense (recall the diagonalization theorems).
– Rebellos
Nov 26 at 7:23
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
That makes sense, thanks!
– user6259845
Nov 26 at 7:24
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
No problem, glad I could help! If the answer was helpful you may use the votes buttons!
– Rebellos
Nov 26 at 7:29
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.
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%2f3013968%2fidentifying-the-first-eigenvector%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
