The paper discusses the method of rank factorization for solving spectral problems for two-parameter polynomial matrices. New forms of rank factorization, which are computed using unimodular matrices only, are suggested. Applications of these factorizations to solving spectral problems for two-parameter polynomial matrices of both general and special forms are presented. In particular, matrices free of the singular spectrum are considered. Conditions sufficient for a matrix to be free of the singular spectrum and also conditions sufficient for a basis matrix of the null-space to have neither the finite regular nor the finite singular spectrum are provided. Bibliography: 3 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Kublanovskaya, “To solving problems of algebra for two-parameter matries. 1,” Zap. Nauhn. Semin, POMI, 359, 107–149 (2008).
V. N. Kublanovskaya and V. B. Khazanov, Numerial Methods for Solwing Parametric Problems of Algebra. Part1. One-Parameter Problems [inRussian], Nauka, St. Petersburg (2004).
V. B. Khazanov, “On some properties of polynomial bases of subspaces over the field of rational funtions in several variables,” Zap. Nauhn. Semin. POMI, 284, 177–191 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 382, 2010, pp. 141–149.
Rights and permissions
About this article
Cite this article
Kublanovskaya, V.N., Khazanov, V.B. To solving problems of algebra for two-parameter matrices. VII. J Math Sci 176, 78–82 (2011). https://doi.org/10.1007/s10958-011-0395-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-011-0395-6