Find nonsingular matrix C such that C^-1AC is a diagonal matrix
lets say A =
[ 1 0 ]
[ 1 3 ]
I know some properties like the DET will be the same and they have same eigenvalues. I also know if the basis of B (or C^--1AC) is U and the bases for A is E, then U = AE.
However, I don't know how to put all of this together to get the answer. How would I even get the basis of a matrix?