Mixing
Determining values of multilinear forms/ differential forms
$begingroup$
I started getting into the topic of multilinear forms and differential forms.
I find it quite hard to get into.
if I solve $$ Phi ( begin{pmatrix} 1 \ 2\3 end{pmatrix} , begin{pmatrix} 4 \5\6 end{pmatrix}) $$
$n=3 , Phi= triangle_{(1,2)}-2 triangle_{(1,3)}+ 3 triangle_{(2,3)} $
Is this way right?:
$$ begin{vmatrix} 1 & 4\ 2& 5 end{vmatrix} - 2 begin{vmatrix} 1 & 4\ 3 & 6 end{vmatrix} +3 begin{vmatrix} 2 & 5\ 3 & 6 end{vmatrix}= -3+12-9=0$$
I am not sure how to deal with :
$$ ( df )( pi , 0, frac12 ) (begin{pmatrix} -1 \ frac{1}{ pi} \ sqrt{3} end{pmatrix} )$$
where $n=3 $ and
$ f(x,y,z)= sin x+e^y arccos z $
any ideas?
real-analysis multilinear-algebra
edited Jan 9 at 22:10
janmarqz
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
$endgroup$
add a comment |
$begingroup$
I started getting into the topic of multilinear forms and differential forms.
I find it quite hard to get into.
if I solve $$ Phi ( begin{pmatrix} 1 \ 2\3 end{pmatrix} , begin{pmatrix} 4 \5\6 end{pmatrix}) $$
$n=3 , Phi= triangle_{(1,2)}-2 triangle_{(1,3)}+ 3 triangle_{(2,3)} $
Is this way right?:
$$ begin{vmatrix} 1 & 4\ 2& 5 end{vmatrix} - 2 begin{vmatrix} 1 & 4\ 3 & 6 end{vmatrix} +3 begin{vmatrix} 2 & 5\ 3 & 6 end{vmatrix}= -3+12-9=0$$
I am not sure how to deal with :
$$ ( df )( pi , 0, frac12 ) (begin{pmatrix} -1 \ frac{1}{ pi} \ sqrt{3} end{pmatrix} )$$
where $n=3 $ and
$ f(x,y,z)= sin x+e^y arccos z $
any ideas?
real-analysis multilinear-algebra
edited Jan 9 at 22:10
janmarqz
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
$endgroup$
2
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
1
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18
add a comment |
$begingroup$
I started getting into the topic of multilinear forms and differential forms.
I find it quite hard to get into.
if I solve $$ Phi ( begin{pmatrix} 1 \ 2\3 end{pmatrix} , begin{pmatrix} 4 \5\6 end{pmatrix}) $$
$n=3 , Phi= triangle_{(1,2)}-2 triangle_{(1,3)}+ 3 triangle_{(2,3)} $
Is this way right?:
$$ begin{vmatrix} 1 & 4\ 2& 5 end{vmatrix} - 2 begin{vmatrix} 1 & 4\ 3 & 6 end{vmatrix} +3 begin{vmatrix} 2 & 5\ 3 & 6 end{vmatrix}= -3+12-9=0$$
I am not sure how to deal with :
$$ ( df )( pi , 0, frac12 ) (begin{pmatrix} -1 \ frac{1}{ pi} \ sqrt{3} end{pmatrix} )$$
where $n=3 $ and
$ f(x,y,z)= sin x+e^y arccos z $
any ideas?
real-analysis multilinear-algebra
edited Jan 9 at 22:10
janmarqz
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
$endgroup$
I started getting into the topic of multilinear forms and differential forms.
I find it quite hard to get into.
if I solve $$ Phi ( begin{pmatrix} 1 \ 2\3 end{pmatrix} , begin{pmatrix} 4 \5\6 end{pmatrix}) $$
$n=3 , Phi= triangle_{(1,2)}-2 triangle_{(1,3)}+ 3 triangle_{(2,3)} $
Is this way right?:
$$ begin{vmatrix} 1 & 4\ 2& 5 end{vmatrix} - 2 begin{vmatrix} 1 & 4\ 3 & 6 end{vmatrix} +3 begin{vmatrix} 2 & 5\ 3 & 6 end{vmatrix}= -3+12-9=0$$
I am not sure how to deal with :
$$ ( df )( pi , 0, frac12 ) (begin{pmatrix} -1 \ frac{1}{ pi} \ sqrt{3} end{pmatrix} )$$
where $n=3 $ and
$ f(x,y,z)= sin x+e^y arccos z $
any ideas?
real-analysis multilinear-algebra
real-analysis multilinear-algebra
edited Jan 9 at 22:10
janmarqz
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
edited Jan 9 at 22:10
janmarqz
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
edited Jan 9 at 22:10
janmarqz
6,21241630
edited Jan 9 at 22:10
janmarqz
6,21241630
edited Jan 9 at 22:10
janmarqz
6,21241630
6,21241630
asked Jan 8 at 15:11
constant94constant94
6310
asked Jan 8 at 15:11
constant94constant94
6310
asked Jan 8 at 15:11
constant94constant94
6310
6310
2
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
1
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18
add a comment |
2
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
1
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18
2
2
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
1
1
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18
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%2f3066283%2fdetermining-values-of-multilinear-forms-differential-forms%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%2f3066283%2fdetermining-values-of-multilinear-forms-differential-forms%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
2
$begingroup$
what is it $triangle$?
$endgroup$
– janmarqz
Jan 8 at 18:50
1
$begingroup$
i have edited my question
$endgroup$
– constant94
Jan 8 at 21:48
$begingroup$
take the gradient of $f$ for $df$, evaluate at $(pi,0,1/2)$ and matrix-multiply with the given column.
$endgroup$
– janmarqz
Jan 9 at 22:09
$begingroup$
You may find my lectures somewhat helpful. See, in particular, the last half of MATH 3510.
$endgroup$
– Ted Shifrin
Jan 9 at 22:18