what does it mean by determinant of Jacobian matrix = 0?
$begingroup$
I have an example:
$$ u={x+yover 1-xy} $$
$$ v = tan^{-1}(x)+tan^{-1}(y) $$
So by calculating the determinant of the Jacobian matrix I get zero. Does it mean there is no functional relationship between u and v? What does $|J|=0$ mean?
calculus linear-algebra jacobian
edited Jan 18 at 4:46
El borito
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
$endgroup$
add a comment |
$begingroup$
I have an example:
$$ u={x+yover 1-xy} $$
$$ v = tan^{-1}(x)+tan^{-1}(y) $$
So by calculating the determinant of the Jacobian matrix I get zero. Does it mean there is no functional relationship between u and v? What does $|J|=0$ mean?
calculus linear-algebra jacobian
edited Jan 18 at 4:46
El borito
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
$endgroup$
add a comment |
$begingroup$
I have an example:
$$ u={x+yover 1-xy} $$
$$ v = tan^{-1}(x)+tan^{-1}(y) $$
So by calculating the determinant of the Jacobian matrix I get zero. Does it mean there is no functional relationship between u and v? What does $|J|=0$ mean?
calculus linear-algebra jacobian
edited Jan 18 at 4:46
El borito
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
$endgroup$
I have an example:
$$ u={x+yover 1-xy} $$
$$ v = tan^{-1}(x)+tan^{-1}(y) $$
So by calculating the determinant of the Jacobian matrix I get zero. Does it mean there is no functional relationship between u and v? What does $|J|=0$ mean?
calculus linear-algebra jacobian
calculus linear-algebra jacobian
edited Jan 18 at 4:46
El borito
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
edited Jan 18 at 4:46
El borito
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
edited Jan 18 at 4:46
El borito
674216
edited Jan 18 at 4:46
El borito
674216
edited Jan 18 at 4:46
El borito
674216
674216
asked Jan 18 at 3:16
Yibei HeYibei He
2139
asked Jan 18 at 3:16
Yibei HeYibei He
2139
asked Jan 18 at 3:16
Yibei HeYibei He
2139
2139
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
In this case, there is a functional relationship between $u$ and $v$: in fact $u = tan(v)$. Thus the transformation $(x,y) to (u,v)$ is not invertible: there is no way to get $x$ and $y$ back from $u$ and $v$.
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
$endgroup$
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%2f3077789%2fwhat-does-it-mean-by-determinant-of-jacobian-matrix-0%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
$begingroup$
In this case, there is a functional relationship between $u$ and $v$: in fact $u = tan(v)$. Thus the transformation $(x,y) to (u,v)$ is not invertible: there is no way to get $x$ and $y$ back from $u$ and $v$.
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
$endgroup$
add a comment |
$begingroup$
In this case, there is a functional relationship between $u$ and $v$: in fact $u = tan(v)$. Thus the transformation $(x,y) to (u,v)$ is not invertible: there is no way to get $x$ and $y$ back from $u$ and $v$.
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
$endgroup$
add a comment |
$begingroup$
In this case, there is a functional relationship between $u$ and $v$: in fact $u = tan(v)$. Thus the transformation $(x,y) to (u,v)$ is not invertible: there is no way to get $x$ and $y$ back from $u$ and $v$.
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
$endgroup$
In this case, there is a functional relationship between $u$ and $v$: in fact $u = tan(v)$. Thus the transformation $(x,y) to (u,v)$ is not invertible: there is no way to get $x$ and $y$ back from $u$ and $v$.
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
answered Jan 18 at 4:36
Robert IsraelRobert Israel
323k23212466
323k23212466
add a comment |
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%2f3077789%2fwhat-does-it-mean-by-determinant-of-jacobian-matrix-0%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
