1. If A is diagonalizable, then the column vectors of the diagonalizing matrix X are eigen vectors of A and the diagonal elements D are corresponding eigenvalues of A
2. The diagonalizing matrix X is not unique.
3. If A is nxn and A has n distinct eigenvalues, then A is diagonalizable. If not distinct, then A may or may not be diagonalizable, depending on whether A has n lin. ind. eigenvectors.
4. If A is diagonalizable, then A can be factored into a product .
To obtain eigenvectors, you need to first get the eigenvalues.
If the eigenvalues are used to form a diagonalizing matrix X, then
A converges to a steady state vector and x is a probability vector.