Mixing
Is working out the smith normal form trivial?
$begingroup$
What's the point of using elementary column operations to work out the smith normal form of a matrix of reals when it is easy to work out exactly how many redundant equations there are from the row reduced matrix, thus identifying the variable s associated with the smith normal form?
linear-algebra matrices
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
$endgroup$
add a comment |
$begingroup$
What's the point of using elementary column operations to work out the smith normal form of a matrix of reals when it is easy to work out exactly how many redundant equations there are from the row reduced matrix, thus identifying the variable s associated with the smith normal form?
linear-algebra matrices
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
$endgroup$
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44
add a comment |
$begingroup$
What's the point of using elementary column operations to work out the smith normal form of a matrix of reals when it is easy to work out exactly how many redundant equations there are from the row reduced matrix, thus identifying the variable s associated with the smith normal form?
linear-algebra matrices
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
$endgroup$
What's the point of using elementary column operations to work out the smith normal form of a matrix of reals when it is easy to work out exactly how many redundant equations there are from the row reduced matrix, thus identifying the variable s associated with the smith normal form?
linear-algebra matrices
linear-algebra matrices
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
asked Jan 20 at 19:47
Dis-integratingDis-integrating
1,038426
1,038426
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44
add a comment |
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44
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%2f3081062%2fis-working-out-the-smith-normal-form-trivial%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%2f3081062%2fis-working-out-the-smith-normal-form-trivial%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
$begingroup$
Could you provide some context? Smith normal form can be obtained in a much more general setting. For instance, one can show the fundamental theorem of finitely generated modules over a principal ideal domain using this form.
$endgroup$
– Dean Young
Jan 21 at 4:44