Finding the minimal polynomial of A with its Characteristic polynomial and dimensions of eigenspaces given.
0
$begingroup$
Let $A$ be a $6times 6$ complex matrix with Characteristic Polynomial, $c_A(x) = (x^2+1)^3$,
$dim E(i) = 2$ and $dim E(-i) = 1$. Find the minimal polynomial of $A$.
linear-algebra minimal-polynomials
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
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add a comment |
0
$begingroup$
Let $A$ be a $6times 6$ complex matrix with Characteristic Polynomial, $c_A(x) = (x^2+1)^3$,
$dim E(i) = 2$ and $dim E(-i) = 1$. Find the minimal polynomial of $A$.
linear-algebra minimal-polynomials
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
$endgroup$
$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
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– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
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– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tagproof-verification.
$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36
add a comment |
0
0
0
$begingroup$
Let $A$ be a $6times 6$ complex matrix with Characteristic Polynomial, $c_A(x) = (x^2+1)^3$,
$dim E(i) = 2$ and $dim E(-i) = 1$. Find the minimal polynomial of $A$.
linear-algebra minimal-polynomials
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
$endgroup$
Let $A$ be a $6times 6$ complex matrix with Characteristic Polynomial, $c_A(x) = (x^2+1)^3$,
$dim E(i) = 2$ and $dim E(-i) = 1$. Find the minimal polynomial of $A$.
linear-algebra minimal-polynomials
linear-algebra minimal-polynomials
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
edited Dec 8 '18 at 0:44
Arturo Magidin
262k34586910
262k34586910
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
asked Dec 8 '18 at 0:18
Ashis JanaAshis Jana
22
22
$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
$endgroup$
– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
$endgroup$
– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tagproof-verification.
$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36
add a comment |
$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
$endgroup$
– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
$endgroup$
– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tagproof-verification.
$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36
$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
$endgroup$
– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
$endgroup$
– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
$endgroup$
– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
$endgroup$
– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tag
proof-verification.$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tag
proof-verification.$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36
add a comment |
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$begingroup$
Welcome to math.stackexchange. Your experience will be improved if instead of simply posting your assigned problem (which you phrase as if you were assigning homework to the site, which you are certainly not doing), you include your thoughts or your attempts and what is causing you problems in trying to solve the problem. The site frowns on people who just post problems with no context, no information about what they’ve tried (or what they know), and no sign of having expended any effort in solving tghe problem themselves.
$endgroup$
– Arturo Magidin
Dec 8 '18 at 0:42
$begingroup$
I am extremely sorry, I thought this site works in that way so i just posted it. Anyway I figured out a way to solve this problem, wanna make sure its correct....here from CP, we get the eigenvalues as i and -i, and the minimal polynomial would be (x-i)^2.(x+i), is this correct?
$endgroup$
– Ashis Jana
Dec 9 '18 at 1:21
$begingroup$
You can post your answer as an edit to your question, and ask for verificaiton. Add the tag
proof-verification.$endgroup$
– Arturo Magidin
Dec 9 '18 at 1:36