On spectral properties of multiparameter polynomial matrices

V. B. Khazanov

Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XI, Tome 229 (1995), pp. 284-321

Résumé

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.