A matrix A belonging tois a square root of B belonging to
=B. Show that every diagonalizable matrix in
I know that a diagonal matrix has all zeros outside of the diagonal and the diagonal may or maynot have zeros. I want to say that these matrices must be similar as well.
I am not sure how to prove this. Any help would be great. Thanks!
Here is the jist of it. If a matrix is diagonalizable then there exists a matrix P such thatOriginally Posted by page929
A matrix A belonging to
I know that a diagonal matrix has all zeros outside of the diagonal and the diagonal may or maynot have zeros. I want to say that these matrices must be similar as well.
I am not sure how to prove this. Any help would be great. Thanks!
where
Now define the matrix B as
Where
Now we have that
(\mathbf{PD}_B\mathbf{P^{-1}})=\mathbf{PD}_B^2\mathbf{P^{-1}}=\mathbf{PD}\mathbf{P^{-1}}=\mathbf{A})
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