On spectral properties of multiparameter polynomial matrices

Spectral problems for multiparameter polynomial matrices are considered. The notions of the spectrum (including those of its finite, infinite, regular, and singular parts), of the analytic multiplicity of a point of the spectrum, of bases of null-spaces, of Jordan $s$-semilattices of vectors and of generating vectors, and of the geometric and complete geometric multiplicities of a point of the spectrum are introduced. The properties of the above characteristics are described. A method for linearizing a polynomial matrix (with respect to one or several parameters) by passing to the accompanying pencils is suggested. The interrelations between spectral characteristics of a polynomial matrix and those of the accompanying pencils are established. Bibliography: 12 titles.