Jordan block size

Clash Royale CLAN TAG#URR8PPP

up vote
3
down vote

favorite

I was wondering about the size of the Jordan blocks of the following matrix.

$$beginbmatrix
0 & 1 & 0\
0 & 0 & 1\
0 & 0 & 0
endbmatrix$$

I know that Jordan blocks have $1$'s on the superdiagonal. So are these $3$ blocks of size $1 times 1$ or is this one block of size $3 times 3$? I'm not sure how to tell the difference. Thanks in advance.

matrices jordan-normal-form

share|cite|improve this question

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

asked Jul 24 at 5:19

user463102

1268

add a comment | 

up vote
3
down vote

favorite

I was wondering about the size of the Jordan blocks of the following matrix.

$$beginbmatrix
0 & 1 & 0\
0 & 0 & 1\
0 & 0 & 0
endbmatrix$$

I know that Jordan blocks have $1$'s on the superdiagonal. So are these $3$ blocks of size $1 times 1$ or is this one block of size $3 times 3$? I'm not sure how to tell the difference. Thanks in advance.

matrices jordan-normal-form

share|cite|improve this question

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

asked Jul 24 at 5:19

user463102

1268

add a comment | 

up vote
3
down vote

favorite

up vote
3
down vote

favorite

I was wondering about the size of the Jordan blocks of the following matrix.

$$beginbmatrix
0 & 1 & 0\
0 & 0 & 1\
0 & 0 & 0
endbmatrix$$

I know that Jordan blocks have $1$'s on the superdiagonal. So are these $3$ blocks of size $1 times 1$ or is this one block of size $3 times 3$? I'm not sure how to tell the difference. Thanks in advance.

matrices jordan-normal-form

share|cite|improve this question

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

asked Jul 24 at 5:19

user463102

1268

I was wondering about the size of the Jordan blocks of the following matrix.

$$beginbmatrix
0 & 1 & 0\
0 & 0 & 1\
0 & 0 & 0
endbmatrix$$

I know that Jordan blocks have $1$'s on the superdiagonal. So are these $3$ blocks of size $1 times 1$ or is this one block of size $3 times 3$? I'm not sure how to tell the difference. Thanks in advance.

matrices jordan-normal-form

share|cite|improve this question

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

asked Jul 24 at 5:19

user463102

1268

share|cite|improve this question

share|cite|improve this question

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

edited Jul 27 at 20:02

Rodrigo de Azevedo

12.6k41751

12.6k41751

asked Jul 24 at 5:19

user463102

1268

asked Jul 24 at 5:19

user463102

1268

asked Jul 24 at 5:19

user463102

1268

1268

add a comment | 

add a comment | 

1 Answer
1

active

oldest

votes

up vote
3
down vote



accepted

If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

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',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2861032%2fjordan-block-size%23new-answer', 'question_page');

);

Post as a guest

Name Email

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
3
down vote



accepted

If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

add a comment | 

up vote
3
down vote



accepted

If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

add a comment | 

up vote
3
down vote



accepted

up vote
3
down vote



accepted

If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

share|cite|improve this answer

share|cite|improve this answer

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

answered Jul 24 at 5:32

Parcly Taxel

33.5k136588

33.5k136588

add a comment | 

add a comment | 

 

draft saved

draft discarded

 

draft saved

draft discarded

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

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2861032%2fjordan-block-size%23new-answer', 'question_page');

);

Post as a guest

Name Email

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

Name Email

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

Name Email

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

Name Email

Name Email

Name

Email

Name Email

Name

Email