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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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Abstract

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.

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Authors
  1. V. M. Petrichkovich
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Additional information

Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 860–862, June, 1997.

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Petrichkovich, V.M. A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations. Ukr Math J 49, 963–965 (1997). https://doi.org/10.1007/BF02513439

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  • DOI: https://doi.org/10.1007/BF02513439

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