To solving problems of algebra for two-parameter matrices. 5

The paper continues the series of papers devoted to surveying and developing methods for solving the following problems for a two-parameter matrix $F(\lambda,\mu)$ of general form: exhausting points of the mixed regular spectrum of $F(\lambda,\mu)$; performing operations on polynomials in two variables (computing the GCD and LCM of a sequence of polynomials, division of polynomials and factorization); computing a minimal basis of the null-space of polynomial solutions of the matrix $F(\lambda,\mu)$ and separation of its regular kernel; inversion and pseudoinversion of polynomial and rational matrices in two variables, and solution of systems of nonlinear algebraic equations in two unknowns. Most of the methods suggested are based on rank factorizations of a two-parameter polynomial matrix and on the method of hereditary pencils. Bibl. – 7 titles.