Are they similar matrix
0
$begingroup$
Do $begin{bmatrix}
0&i&0\0&0&1\0&0&0
end{bmatrix} $ and $begin{bmatrix}
0&0&0\-i&0&0\0&1&0
end{bmatrix} $ are similar.Is this True/false
Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me
linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
$endgroup$
|
show 1 more comment
0
$begingroup$
Do $begin{bmatrix}
0&i&0\0&0&1\0&0&0
end{bmatrix} $ and $begin{bmatrix}
0&0&0\-i&0&0\0&1&0
end{bmatrix} $ are similar.Is this True/false
Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me
linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
$endgroup$
$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
|
show 1 more comment
0
0
0
$begingroup$
Do $begin{bmatrix}
0&i&0\0&0&1\0&0&0
end{bmatrix} $ and $begin{bmatrix}
0&0&0\-i&0&0\0&1&0
end{bmatrix} $ are similar.Is this True/false
Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me
linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
$endgroup$
Do $begin{bmatrix}
0&i&0\0&0&1\0&0&0
end{bmatrix} $ and $begin{bmatrix}
0&0&0\-i&0&0\0&1&0
end{bmatrix} $ are similar.Is this True/false
Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me
linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector
linear-algebra vector-spaces eigenvalues-eigenvectors generalizedeigenvector
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
edited Dec 10 '18 at 6:38
Vasanth Kris
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
asked Dec 10 '18 at 6:19
Vasanth KrisVasanth Kris
6
6
$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
|
show 1 more comment
$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
|
show 1 more comment
1 Answer
1
active
oldest
votes
0
$begingroup$
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?
answered Dec 10 '18 at 6:38
MarkMark
6,568416
$endgroup$
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
0
$begingroup$
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?
answered Dec 10 '18 at 6:38
MarkMark
6,568416
$endgroup$
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
add a comment |
0
$begingroup$
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?
answered Dec 10 '18 at 6:38
MarkMark
6,568416
$endgroup$
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
add a comment |
0
0
0
$begingroup$
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?
answered Dec 10 '18 at 6:38
MarkMark
6,568416
$endgroup$
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?
answered Dec 10 '18 at 6:38
MarkMark
6,568416
answered Dec 10 '18 at 6:38
MarkMark
6,568416
answered Dec 10 '18 at 6:38
MarkMark
6,568416
answered Dec 10 '18 at 6:38
MarkMark
6,568416
6,568416
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
add a comment |
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
I dont know jordan form any other way?
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:41
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Well, that's one of the reasons why people on this forum ask to show what you tried-because that way it will also be clear how much do you know about the problem. I'll try to think of another solution.
$endgroup$
– Mark
Dec 10 '18 at 6:44
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
Btw what is answer true or false.... Next time if i ask i will add details as much as i xan
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:46
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
$begingroup$
They are similar. Matrices of order at most $3times 3$ (not true for higher dimension matrices) are similar if and only if their characteristic and minimal polynomials are the same. I never thought about proving this lemma without Jordan form though.
$endgroup$
– Mark
Dec 10 '18 at 6:48
add a comment |
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$begingroup$
Why negative vote
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:25
$begingroup$
Welcome to MSE! It is more likely that you'll receive an answer if you showed us that you've made an effort
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:38
$begingroup$
Sorry i dont know how to start
$endgroup$
– Vasanth Kris
Dec 10 '18 at 6:39
$begingroup$
Oh don't mind the downvoters, they have a habit of downvoting posts that doesn't show efforts (and without explaining why)
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39
$begingroup$
I've made up for it by upvoting. Just make sure you show that you've tried next time
$endgroup$
– Vee Hua Zhi
Dec 10 '18 at 6:39