Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
A D5107: Triple $(B, D, B^{-1})$ is a diagonal factorization for $A$ if and only if

(1)	$B \in \mathbb{C}^{N \times N}$ is an D5870: Invertible complex matrix
(2)	$D \in \mathbb{C}^{N \times N}$ is a D5858: Diagonal complex matrix
(3)	$B^{-1}$ is an D2089: Inverse matrix for $B$
(4)	\begin{equation} A = B D B^{-1} \end{equation}