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

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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.