Khazanov, V. B. 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. Reviewer: Daniel Kressner (Zagreb) Cited in 4 Documents MSC: 65F30 Other matrix algorithms (MSC2010) 15A54 Matrices over function rings in one or more variables Keywords:multiparameter matrix polynomial; Sylvester matrix; range; null space; Jordan chain PDFBibTeX XMLCite \textit{V. B. Khazanov}, Zap. Nauchn. Semin. POMI 323, 182--214 (2005; Zbl 1086.65038); translation in J. Math. Sci., New York 137, No. 3, 4862--4878 (2007) Full Text: EuDML Link