Minimal indices cancellation and rank revealing factorizations for rational matrix functions
The authors investigate general rational matrix functions, in particular, they consider their finite and infinite poles and zeros, their partial multiplicities and the left (right) indices of a minimal polynomial basis of the null spaces to the left (right). They concentrate on the left minimal displacement problem and the left rank compression problem. The authors obtain the class of minimal solutions to the minimal indices displacement problem formulated for a completely general rational matrix function. They show that minimal indices can be canceled by an invertible factor that may have arbitrary poles and zeros. They study minimal solutions that feature some symmetry with respect to the imaginary axis or the unit circle and have given necessary and sufficient existence conditions and the class of solutions. They also extend the well-known rank revealing factorization from constant to rational matrices.
scientific article; zbMATH DE number 5612556
scientific article