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diagonal matrices P6 watch

1. I suppose everyone is thinking that I know absolutely no P6 maths... well, you're probably correct. Anyway, I'm LEARNING...

Given that the matrix P is such that P^(-1)AP is a diagonal matrix B, write down a possible form for B.

A =

4 -2 0
-2 0 -2
0 -2 1

So, what's a diagonal matrix anyway, and how does one do this?
2. (Original post by lesser weevil)
I suppose everyone is thinking that I know absolutely no P6 maths... well, you're probably correct. Anyway, I'm LEARNING...

Given that the matrix P is such that P^(-1)AP is a diagonal matrix B, write down a possible form for B.

A =

4 -2 0
-2 0 -2
0 -2 1

So, what's a diagonal matrix anyway, and how does one do this?
A diagonal matrix 3x3 is one of the form

a 0 0
0 b 0
0 0 c

In the question you have then P has three independent eigenvectors as its columns and P^(-1)AP is a diagonal matrix with the eigenvalues down the diagonal

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