Thread: Diagonalization

Let 0-2 46 .
q: Find formulas for the entries of , where is a positive integer.

I found eigenvalues, 2 and 4, then found their corresponding eigenspaces.

D^n=(P^-1)(A^n)P
=
2^n-2 0
8^n
.
Which is incorrect. Can someone please help?

Originally Posted by krtica

Let 0-2 46 .
q: Find formulas for the entries of , where is a positive integer.

I found eigenvalues, 2 and 4, then found their corresponding eigenspaces.

D^n=(P^-1)(A^n)P
=
2^n-2 0
8^n
.
Which is incorrect. Can someone please help?

What does this notation mean?

I apologize, the format didn't turn out as I expected. It is a 2x2 matrix. The first row is 2^n, -2. The second row is 0, 8^n.

D=(P^-1)AP, where P is a basis for both Eigenspaces with eigenvalues of 2 and 4. A is for the original matrix.

and correct?

Yes, that's correct.

where D is the a diagonal matrix of the eigenvalues and X is the matrix with the corresponding eigenvectors.

Thank you. I really, really appreciate your help.