How do I show that every square complex matrix A can be expressed as a sum of diagonalizable matrix B and nilpotent matrix C?
I don't know hot to express diagonalizable matrix generally beyond B=PDP-1, and I can't express nilpotent matrix either. To me these seem like they could be anything. I don't see any rule of the thumb on "How should a diagonalizable/nilpotent matrix look like".
I don't know hot to express diagonalizable matrix generally beyond B=PDP-1, and I can't express nilpotent matrix either. To me these seem like they could be anything. I don't see any rule of the thumb on "How should a diagonalizable/nilpotent matrix look like".