A REAL-CONINVOLUTORY ANALOG OF THE POLAR DECOMPOSITION

We study properties of coninvolutory matrices (EEBAR = I), and derive a canonical form under similarity as well as a canonical form under un itary consimilarity for them. We show that any complex matrix has a co ninvolutory dilation, and we characterize the minimum size of a coninv olutory dilation of a square matrix. We characterize the m-by-n comple x matrices A that can be factored as A = RE with R real and E coninvol utory, and we discuss the uniqueness of this factorization when A is s quare and nonsingular.