Title: Diagonalizability with respect to perplectic and pseudo-unitary similarity transformations
Abstract: Let Rn be the n-by-n backward identity matrix and let Ln,k:=Ik⊕−In−k. Suppose A∈Cn×n is nonsingular. We say that A is perplectic if RnATRn=A−1; and A is pseudo-unitary if Ln,kA⁎Ln,k=A−1. We give necessary and sufficient conditions for a matrix to be diagonalizable via a perplectic or a pseudo-unitary matrix.