orthogonal complement of subspace
$begingroup$
I am not a mathematician but I faced the following problem when I want to apply some machine learning algorithm to solve nlp problem.
let say that I have a matrix $A$ that is $100X50$ and I project each row to a $5$ dimension subspace to produce the Matrix $A_5$ which is $100X5$, now how I can find the reminder $45$ dim subspace of $A$ (which is $100X45$ of $A$ ) that is orthogonal to $A_5$.
I would appreciate any help
vector-spaces orthogonality
edited Jan 6 at 18:05
Sauhard Sharma
953318
asked Jan 6 at 17:52
AbrarAbrar
12
$endgroup$
add a comment |
$begingroup$
I am not a mathematician but I faced the following problem when I want to apply some machine learning algorithm to solve nlp problem.
let say that I have a matrix $A$ that is $100X50$ and I project each row to a $5$ dimension subspace to produce the Matrix $A_5$ which is $100X5$, now how I can find the reminder $45$ dim subspace of $A$ (which is $100X45$ of $A$ ) that is orthogonal to $A_5$.
I would appreciate any help
vector-spaces orthogonality
edited Jan 6 at 18:05
Sauhard Sharma
953318
asked Jan 6 at 17:52
AbrarAbrar
12
$endgroup$
add a comment |
$begingroup$
I am not a mathematician but I faced the following problem when I want to apply some machine learning algorithm to solve nlp problem.
let say that I have a matrix $A$ that is $100X50$ and I project each row to a $5$ dimension subspace to produce the Matrix $A_5$ which is $100X5$, now how I can find the reminder $45$ dim subspace of $A$ (which is $100X45$ of $A$ ) that is orthogonal to $A_5$.
I would appreciate any help
vector-spaces orthogonality
edited Jan 6 at 18:05
Sauhard Sharma
953318
asked Jan 6 at 17:52
AbrarAbrar
12
$endgroup$
I am not a mathematician but I faced the following problem when I want to apply some machine learning algorithm to solve nlp problem.
let say that I have a matrix $A$ that is $100X50$ and I project each row to a $5$ dimension subspace to produce the Matrix $A_5$ which is $100X5$, now how I can find the reminder $45$ dim subspace of $A$ (which is $100X45$ of $A$ ) that is orthogonal to $A_5$.
I would appreciate any help
vector-spaces orthogonality
vector-spaces orthogonality
edited Jan 6 at 18:05
Sauhard Sharma
953318
asked Jan 6 at 17:52
AbrarAbrar
12
edited Jan 6 at 18:05
Sauhard Sharma
953318
asked Jan 6 at 17:52
AbrarAbrar
12
edited Jan 6 at 18:05
Sauhard Sharma
953318
edited Jan 6 at 18:05
Sauhard Sharma
953318
edited Jan 6 at 18:05
Sauhard Sharma
953318
953318
asked Jan 6 at 17:52
AbrarAbrar
12
asked Jan 6 at 17:52
AbrarAbrar
12
asked Jan 6 at 17:52
AbrarAbrar
12
12
add a comment |
add a comment |
0
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%2f3064180%2forthogonal-complement-of-subspace%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
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.
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%2f3064180%2forthogonal-complement-of-subspace%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
