On Semiscalar and Quasidiagonal Equivalences of Matrices - Shavarovskyy, B. Z. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
For a certain class of polynomial matrices A(x), we consider transformations S A(x) R(x) with invertible matrices S and R(x), i.e., the so-called semiscalarly equivalent transformations. We indicate necessary and sufficient conditions for this type of equivalence of matrices. We introduce the notion of quasidiagonal equivalence of numerical matrices. We establish the relationship between the semiscalar and quasidiagonal equivalences and the problem of matrix pairs.