1. eigenvalues

1. Let A be nxn matrix, suppose that $\displaystyle A \ne 0,I,A^2 = A$ so prove that $\displaystyle \lambda = 1,\lambda = 0$ are eigenvalues.

2. if I know that A and B are similar how can I find P invertibale that sustains: $\displaystyle B = P^{ - 1} AP$?

2. Originally Posted by omert
1. Let A be nxn matrix, suppose that $\displaystyle A \ne 0,I,A^2 = A$ so prove that $\displaystyle \lambda = 1,\lambda = 0$ are eigenvalues.
$\displaystyle Ax = \lambda x \implies A^2 x = \lambda Ax = \lambda ^2 x$ But $\displaystyle A^2 = A \implies \lambda x = Ax = \lambda ^2 x$. This means $\displaystyle \lambda^2 = \lambda$

2. if I know that A and B are similar how can I find P invertibale that sustains: $\displaystyle B = P^{ - 1} AP$?
Isnt that the definition?

3. Quote:
2. if I know that A and B are similar how can I find P invertibale that sustains: ?
Isnt that the definition?
I wanted to know, that in case that I know A and B, and I know that they are similar, how can I find P