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


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.


Principal Ideal Polynomial Matrice Invertible Matrice Nonsingular Matrice Matrix Adjoint 
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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. M. Petrichkovich

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