Projection onto intersection of affine subspaces
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 at 19:59
InspectorPing
1148
add a comment |
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 at 19:59
InspectorPing
1148
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33
add a comment |
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
asked Nov 15 at 19:59
InspectorPing
1148
I was wondering if there is a closed formular for the projection onto the intersection of the subspaces $Ax = b$ and $Zx = 0$. I know there is a closed formula for either one of those, but can you also project onto the interesection by use of the pseudoinverse?
I am aware of the alternating projection method, but this takes too long for my purposes.
Thanks!
linear-algebra
linear-algebra
asked Nov 15 at 19:59
InspectorPing
1148
asked Nov 15 at 19:59
InspectorPing
1148
asked Nov 15 at 19:59
InspectorPing
1148
asked Nov 15 at 19:59
InspectorPing
1148
asked Nov 15 at 19:59
InspectorPing
1148
1148
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33
add a comment |
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33
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%2f3000229%2fprojection-onto-intersection-of-affine-subspaces%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%2f3000229%2fprojection-onto-intersection-of-affine-subspaces%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
Since the intersection of affine subspaces is affine, is there any reason that this does not answer your question? math.stackexchange.com/questions/1320363/…
– aleph_two
Dec 17 at 4:23
Yes, what takes the place of $A$ in this case. Since my subspace is now the intersection of the spaces above, what is the matrix $A$ of which I can compute the generalized inverse now? It is neither $Ax = b$ nor $Zx = 0$ anymore.
– InspectorPing
Dec 17 at 14:33