# Thread: cayley hamilton theorem problem...

1. ## cayley hamilton theorem problem...

Hello I have a small problem and I am wondering if someone could help me with Cayley Hamilton Theorem..please!

Let D = [4 0 0, 0 -1 0, 0 0 9]. Find a matrix D^1/2 E M(3x3) (C) such that

D^1/2 * D^1/2 = D...

I know we have to use this product....

A = VDV^-1....and A^k = VD^kv-1....for example A^2 = VD^2V^-1...

But I cant take the square root of the D and its elements because it contains -1 as one of its elements...

thanks a lot!

2. This could be really bone-headed, but doesn't

work? It's a bit hard to read your syntax (MathGuru will hopefully fix LaTeX soon!), but this matrix is definitely in the space of 3 x 3 matrices over the complexes, which is what it looks like your space is.

3. i prefer √D =

[-2 0 0]
[ 0 -i 0]
[0 0 -3] and you can't make me change my mind.

4. Or I suppose you could do any one of the eight possible solutions, right? I don't know of any others.

5. one hopes that is why the author of the book in which the problem presumably occurs said "a" matrix, instead of "the" matrix (take the blue pill...)

6. sir! thanks for the response but I still dont get how you ended up getting that matrix....using cayley hamilton matrix??