orthogonality relation

Dear iMechanica members,

I deal with exteded Stroh formalism for piezoelectric media. I have problems with orthogonalization of Stroh´s matrices A, B, respectively how to fulfil the ortogonality relations (see attachments). I tried to "rape" it and made the left matrix inverse of the right matrix (then the product is an unit matrix) and I became very similar singularity expomemt as in the paper