Procrustes problems for (P,Q,η)(P,Q,η)-reflexive matrices

This paper characterizes (P,Q,η)(P,Q,η)-reflexive matrices, showing that a (P,Q,η)(P,Q,η)-reflexive matrix can be represented in terms of kk matrices Aa,b∈Cma×nbAa,b∈Cma×nb, where a+b=η(modk), mama and nbnb are dimensions of the τaτa- and τbτb-eigenspaces of PP and QQ, respectively. A general solution of Procrustes problems of (P,Q,η)(P,Q,η)-reflexive matrices is presented in terms of lower-order matrices A1,η−1,…,Aη−1,1,Aη,k,Aη+1,k−1,…,Ak,ηA1,η−1,…,Aη−1,1,Aη,k,Aη+1,k−1,…,Ak,η under the condition that PP and QQ are unitary.