1. ## Matrices

Hello,
I was wondering if there is a general rule for power positive matrices? I typed "power positive matrices" and searched for it, but to my surprise I couldn't find any general rules/laws explaining how to calculate the power of a matrix; e.g. A^4 or A^5 in 2x2 matrices.

I hope you can understand my question!

Just as with real numbers, exponentiation of matrices (with positive integer powers) indicates repeated multiplication: $A^4 = AAAA\text.$ If you are dealing with diagonal matrices (i.e., square matrices whose only nonzero entries are along the main diagonal), exponentiation can be performed simply by taking the powers of the diagonal entries.