Is a square zero matrix positive semidefinite?Algorithm for generating positive semidefinite matricesinequality-positive semidefinite matricesProve that every positive semidefinite matrix has nonnegative eigenvaluesEigenvalues and positive semidefiniteness of a special matrixHow to make a matrix positive semidefinite?Singularity positive semidefiniteSemidefinite matrix or indefinite?Can strict positive square matrix contain non zero same eigenvaluesThe square root of a positive semidefinite matrixSum of rank 1 positive semidefinite and negative semidefinite matrices
What is it called when someone votes for an option that's not their first choice?
Why is "la Gestapo" feminine?
Are hand made posters acceptable in Academia?
Did Nintendo change its mind about 68000 SNES?
Why do I have a large white artefact on the rendered image?
How can I create URL shortcuts/redirects for task/diff IDs in Phabricator?
Is VPN a layer 3 concept?
Is there any common country to visit for uk and schengen visa?
Is "inadequate referencing" a euphemism for plagiarism?
Should a narrator ever describe things based on a characters view instead of fact?
Can "few" be used as a subject? If so, what is the rule?
Why is indicated airspeed rather than ground speed used during the takeoff roll?
Norwegian Refugee travel document
10 year ban after applying for a UK student visa
Homology of the fiber
Weird lines in Microsoft Word
Don't understand why (5 | -2) > 0 is False where (5 or -2) > 0 is True
What is the tangent at a sharp point on a curve?
Does Shadow Sorcerer's Eyes of the Dark work on all magical darkness or just his/hers?
Do I need to convey a moral for each of my blog post?
Turning a hard to access nut?
Does fire aspect on a sword, destroy mob drops?
Why does Surtur say that Thor is Asgard's doom?
Would mining huge amounts of resources on the Moon change its orbit?
Is a square zero matrix positive semidefinite?
Algorithm for generating positive semidefinite matricesinequality-positive semidefinite matricesProve that every positive semidefinite matrix has nonnegative eigenvaluesEigenvalues and positive semidefiniteness of a special matrixHow to make a matrix positive semidefinite?Singularity positive semidefiniteSemidefinite matrix or indefinite?Can strict positive square matrix contain non zero same eigenvaluesThe square root of a positive semidefinite matrixSum of rank 1 positive semidefinite and negative semidefinite matrices
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
add a comment |
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
add a comment |
$begingroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
$endgroup$
Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?
linear-algebra matrices positive-semidefinite
linear-algebra matrices positive-semidefinite
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
edited 3 hours ago
Kay
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
asked 4 hours ago
KayKay
617
617
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 3 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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%2f3153187%2fis-a-square-zero-matrix-positive-semidefinite%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 3 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 3 hours ago
Gary MoonGary Moon
31613
$endgroup$
add a comment |
$begingroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 3 hours ago
Gary MoonGary Moon
31613
$endgroup$
The $n times n$ zero matrix is positive semidefinite and negative semidefinite.
answered 3 hours ago
Gary MoonGary Moon
31613
answered 3 hours ago
Gary MoonGary Moon
31613
answered 3 hours ago
Gary MoonGary Moon
31613
answered 3 hours ago
Gary MoonGary Moon
31613
31613
add a comment |
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
add a comment |
$begingroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
$endgroup$
"When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
answered 3 hours ago
user247327user247327
11.4k1516
11.4k1516
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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%2f3153187%2fis-a-square-zero-matrix-positive-semidefinite%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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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');
var $window = $(window),
onScroll = function(e)
var $elem = $('.new-login-left'),
docViewTop = $window.scrollTop(),
docViewBottom = docViewTop + $window.height(),
elemTop = $elem.offset().top,
elemBottom = elemTop + $elem.height();
if ((docViewTop elemBottom))
StackExchange.using('gps', function() StackExchange.gps.track('embedded_signup_form.view', location: 'question_page' ); );
$window.unbind('scroll', onScroll);
;
$window.on('scroll', onScroll);
);
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
