Consider all linear systems with exactly one eigenvalue equal to 0. Which of these systems are conjugate?
This question considers non-hyperbolic matrices (2x2), which is not covered in our textbook. Basically the problem I think tries to get us to think about conjugacy patterns of these cases, but I am stuck.
If A= ((a, b), (c, d)) a 2x2 has 1 eigenvalue = 0, then I believe c or b must be 0.
So A = ((a, 0), (c, d)) or ((a, b), (0, d)), but I'm not sure where to go from there.
matrices
asked Oct 30 at 2:34
MathGuyForLife
1007
add a comment |
This question considers non-hyperbolic matrices (2x2), which is not covered in our textbook. Basically the problem I think tries to get us to think about conjugacy patterns of these cases, but I am stuck.
If A= ((a, b), (c, d)) a 2x2 has 1 eigenvalue = 0, then I believe c or b must be 0.
So A = ((a, 0), (c, d)) or ((a, b), (0, d)), but I'm not sure where to go from there.
matrices
asked Oct 30 at 2:34
MathGuyForLife
1007
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15
add a comment |
This question considers non-hyperbolic matrices (2x2), which is not covered in our textbook. Basically the problem I think tries to get us to think about conjugacy patterns of these cases, but I am stuck.
If A= ((a, b), (c, d)) a 2x2 has 1 eigenvalue = 0, then I believe c or b must be 0.
So A = ((a, 0), (c, d)) or ((a, b), (0, d)), but I'm not sure where to go from there.
matrices
asked Oct 30 at 2:34
MathGuyForLife
1007
This question considers non-hyperbolic matrices (2x2), which is not covered in our textbook. Basically the problem I think tries to get us to think about conjugacy patterns of these cases, but I am stuck.
If A= ((a, b), (c, d)) a 2x2 has 1 eigenvalue = 0, then I believe c or b must be 0.
So A = ((a, 0), (c, d)) or ((a, b), (0, d)), but I'm not sure where to go from there.
matrices
matrices
asked Oct 30 at 2:34
MathGuyForLife
1007
asked Oct 30 at 2:34
MathGuyForLife
1007
asked Oct 30 at 2:34
MathGuyForLife
1007
asked Oct 30 at 2:34
MathGuyForLife
1007
asked Oct 30 at 2:34
MathGuyForLife
1007
1007
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15
add a comment |
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15
add a comment |
1 Answer
1
active
oldest
votes
This means that the matrix has rank 1 or one row is a multiple of another row and one row is non zero. Formally$$k_1(a,b)+k_2(c,d)=0$$and $$a^2+b^2+c^2+d^2ne 0$$
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
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');
});
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%2f2977032%2fconsider-all-linear-systems-with-exactly-one-eigenvalue-equal-to-0-which-of-the%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
This means that the matrix has rank 1 or one row is a multiple of another row and one row is non zero. Formally$$k_1(a,b)+k_2(c,d)=0$$and $$a^2+b^2+c^2+d^2ne 0$$
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
add a comment |
This means that the matrix has rank 1 or one row is a multiple of another row and one row is non zero. Formally$$k_1(a,b)+k_2(c,d)=0$$and $$a^2+b^2+c^2+d^2ne 0$$
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
add a comment |
This means that the matrix has rank 1 or one row is a multiple of another row and one row is non zero. Formally$$k_1(a,b)+k_2(c,d)=0$$and $$a^2+b^2+c^2+d^2ne 0$$
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
This means that the matrix has rank 1 or one row is a multiple of another row and one row is non zero. Formally$$k_1(a,b)+k_2(c,d)=0$$and $$a^2+b^2+c^2+d^2ne 0$$
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
answered Nov 24 at 18:32
Mostafa Ayaz
13.7k3836
13.7k3836
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f2977032%2fconsider-all-linear-systems-with-exactly-one-eigenvalue-equal-to-0-which-of-the%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
Why did you believe this? Counterexample $$ boldsymbol A = begin{bmatrix}1&1\1&1 end{bmatrix}. $$
– xbh
Oct 30 at 3:13
Ah yes, sorry. Shows my inexperience with linear algebra!
– MathGuyForLife
Oct 30 at 3:15