2017
Том 69
№ 9

All Issues

A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations

Petrichkovich V. M.

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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.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 6, pp 963-965.

Citation Example: 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. Mat. Zh. - 1997. - 49, № 6. - pp. 860–862.

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