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Ukrainian Mathematical Journal

, Volume 49, Issue 6, pp 963–965 | Cite as

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

  • V. M. Petrichkovich
Brief Communications

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.

Keywords

Principal Ideal Polynomial Matrice Invertible Matrice Nonsingular Matrice Matrix Adjoint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. M. Petrichkovich

There are no affiliations available

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