We investigate the structure of polynomial matrices in connection with their reducibility by semiscalarequivalent transformations to simpler forms. We obtain a system of invariants for one class of matrices with respect to semiscalar equivalence. On this basis, we establish the almost canonical form of a matrix with respect to semiscalar equivalence.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 3, pp. 7–20, July–September, 2012.
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Shavarovskii, B.Z. On the Triangular Form of a Polynomial Matrix and Its Invariants with Respect to the Semiscalar Equivalence. J Math Sci 194, 133–148 (2013). https://doi.org/10.1007/s10958-013-1514-3
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DOI: https://doi.org/10.1007/s10958-013-1514-3