Some results on matrix symmetries and a pattern recognition application

This correspondence deals with various matrix symmetries frequently encountered in practice. It is shown that the class of doubly symmetric matrices is not closed under multiplication, whereas centrosymmetric matrices form an Abelian group under addition and a non-Abelian group under multiplication. Results similar to centrosymmetric matrices are presented for the special case of centro-Hermitian matrices. A brief discussion of a pattern recognition feature selection problem is included to demonstrate the manner in which these results may be utilized in practice for developing computationally efficient algorithms.