# eigenvalues

Joined Dec 29, 2004
83
Hi, I need help for this problem:

Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix:
A-1

We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A
Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns)

Does someone has any idea??
Thank you
B

#### cookevillain

Joined Dec 1, 2005
4
Hi,

I am afraid it is too late to answer this question as it was posted a month ago. But just in case.
The eigenvectors will be the same but the eigenvalues will be the reciprocals of those for the original matrix (assuming A-1 is the inverse of A). It all follows from this simple computation:

Ax = bx => A-1(Ax) = A-1bx => x = b A-1x => (1/b)x = A-1x (so x is an eigenvector of A with evalue 1/b)

privided x is an eigenvector of A with eigenvalue b.
Good luck.

C-villain

Originally posted by braddy@Nov 2 2005, 12:11 PM
Hi, I need help for this problem:

Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix:
A-1

We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A
Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns)

Does someone has any idea??
Thank you
B
[post=11424]Quoted post[/post]​