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A resultant approach to computing vector characteristics of multiparameter polynomial matrices. (Russian, English) Zbl 1086.65038

Zap. Nauchn. Semin. POMI 323, 182-214 (2005); translation in J. Math. Sci., New York 137, No. 3, 4862-4878 (2007).
This paper is concerned with a multi-parameter matrix polynomial \(F(\lambda_1, \dots, \lambda_q)\). The notion of resultant matrices, a well-established concept to address one-parameter polynomials, is extended to the multi-parameter case. Besides leading to new methods for computing bases of the range and null space of \(F\), it is shown how the Jordan chain belonging to a spectral point of \(F\) can be extracted from the resultant matrix.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A54 Matrices over function rings in one or more variables
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