Procrustes problems for [formula omitted]-reflexive matrices

Abstract

This paper characterizes ( P , Q , η ) -reflexive matrices, showing that a ( P , Q , η ) -reflexive matrix can be represented in terms of k matrices A a , b ∈ C m a × n b , where a + b = η ( mod k ) , m a and n b are dimensions of the τ a - and τ b -eigenspaces of P and Q , respectively. A general solution of Procrustes problems of ( P , Q , η ) -reflexive matrices is presented in terms of lower-order matrices A 1 , η − 1 , … , A η − 1 , 1 , A η , k , A η + 1 , k − 1 , … , A k , η under the condition that P and Q are unitary.