Similar matrices

  • Thread starter cutesteph
  • Start date
  • #1
63
0

Homework Statement


A=[a,1;0,a] B=[a,0;0,a]
If I want to show if matrix A is NOT similar to matrix B. Is it enough to show that B=/=Inv(P)*A*P? Or would I need to show that they do not have both the same eigenvalues and corresponding eigenvectors?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619

Homework Statement


A=[a,1;0,a] B=[a,0;0,a]
If I want to show if matrix A is NOT similar to matrix B. Is it enough to show that B=/=Inv(P)*A*P? Or would I need to show that they do not have both the same eigenvalues and corresponding eigenvectors?

It would be enough to show B=/=Inv(P)*A*P for any invertible matrix P, if you have a clever way to do that. But I think the eigenvalue/eigenvector approach is more straightforward. If you calculate those for each matrix what do you get?
 

Related Threads on Similar matrices

  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
7
Views
7K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
3
Views
4K
Top