A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations
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We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent.
KeywordsPrincipal Ideal Polynomial Matrice Invertible Matrice Nonsingular Matrice Matrix Adjoint
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- 1.P. S. Kazimirskii and V. M. Petrichkovich, “On the equivalence of polynomial matrices,” in: Theoretical and Applied Problems of Algebra and Differential Equations [in Russian], Naukova Dumka, Kiev (1977), pp. 61–66.Google Scholar