Transformation Law for Tensor of Rank Two
$begingroup$
Okay, I am sorry if this question seems absurd, but I am really having a difficult time understanding it.
In the book by H. Jeffreys chapter Cartesian tensors, he defines a second order tensor as $ omega_{jl},' = a_{ij}, a_{kl},omega_{ik}$.
Then he goes on to demonstrate that we change the variables 'j' and 'l' in the equation , and also shows "dummy indices" can be changed without any trouble, after which he arrives at $ omega_{lj},' = a_{kl}, a_{ij},omega_{ki}$ which makes sense, then in the same line he says that $ omega_{lj},' = a_{ij}, a_{kl},omega_{ki}$.
Which is a bit troubling for me, because $a_{ij}$ and $a_{kl} $ are transformation matrices(like operators), and the order of application is important.
tensor-products
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
$endgroup$
add a comment |
$begingroup$
Okay, I am sorry if this question seems absurd, but I am really having a difficult time understanding it.
In the book by H. Jeffreys chapter Cartesian tensors, he defines a second order tensor as $ omega_{jl},' = a_{ij}, a_{kl},omega_{ik}$.
Then he goes on to demonstrate that we change the variables 'j' and 'l' in the equation , and also shows "dummy indices" can be changed without any trouble, after which he arrives at $ omega_{lj},' = a_{kl}, a_{ij},omega_{ki}$ which makes sense, then in the same line he says that $ omega_{lj},' = a_{ij}, a_{kl},omega_{ki}$.
Which is a bit troubling for me, because $a_{ij}$ and $a_{kl} $ are transformation matrices(like operators), and the order of application is important.
tensor-products
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
$endgroup$
add a comment |
$begingroup$
Okay, I am sorry if this question seems absurd, but I am really having a difficult time understanding it.
In the book by H. Jeffreys chapter Cartesian tensors, he defines a second order tensor as $ omega_{jl},' = a_{ij}, a_{kl},omega_{ik}$.
Then he goes on to demonstrate that we change the variables 'j' and 'l' in the equation , and also shows "dummy indices" can be changed without any trouble, after which he arrives at $ omega_{lj},' = a_{kl}, a_{ij},omega_{ki}$ which makes sense, then in the same line he says that $ omega_{lj},' = a_{ij}, a_{kl},omega_{ki}$.
Which is a bit troubling for me, because $a_{ij}$ and $a_{kl} $ are transformation matrices(like operators), and the order of application is important.
tensor-products
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
$endgroup$
Okay, I am sorry if this question seems absurd, but I am really having a difficult time understanding it.
In the book by H. Jeffreys chapter Cartesian tensors, he defines a second order tensor as $ omega_{jl},' = a_{ij}, a_{kl},omega_{ik}$.
Then he goes on to demonstrate that we change the variables 'j' and 'l' in the equation , and also shows "dummy indices" can be changed without any trouble, after which he arrives at $ omega_{lj},' = a_{kl}, a_{ij},omega_{ki}$ which makes sense, then in the same line he says that $ omega_{lj},' = a_{ij}, a_{kl},omega_{ki}$.
Which is a bit troubling for me, because $a_{ij}$ and $a_{kl} $ are transformation matrices(like operators), and the order of application is important.
tensor-products
tensor-products
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
asked Dec 3 '18 at 21:59
Ashutosh SinghAshutosh Singh
32
32
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%2f3024745%2ftransformation-law-for-tensor-of-rank-two%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%2f3024745%2ftransformation-law-for-tensor-of-rank-two%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
