Extending Results from Orthogonal Matrices to the Class of P -orthogonal Matrices

We extend results concerning orthogonal matrices to a more general class of matrices that will be called P -orthogonal. This is a large class of matrices that includes, for instance, orthogonal and symplectic matrices as particular cases. We study the elementary properties of P -orthogonal matrices and give some exponential representations. The role of these matrices in matrix decompositions, with particular emphasis on generalized polar decompositions, is analysed. An application to matrix equations is presented. Key-words: P -orthogonal, P -symmetric, P -skew-symmetric, generalized polar decompositions, primary matrix functions ∗Work supported in part by ISR and a PRODEP grant, under Concurso n. 4/5.3/PRODEP/2000. †Work supported in part by ISR and research network contract ERB FMRXCT-970137.