Let A be the matrix:
Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A.
DetA - xI
(A-[itex]\lambda[/itex]I)v = 0
The Attempt at a Solution
So, I found DetA- xI, which gave me the eigenvalues 4 and 1. I found the eigenvectors for each value, giving me X =
Now what confuses me is finding the square root of A. I understand that XD1/2X-1 will give me that, so would I just multiply X by D1/2 , and then by X-1? I tried that, and it gave me A=