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

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.
Published
25.06.1997
How to Cite
PetrichkovichV. M. “A Criterion of Diagonalizability of a Pair of Matrices over the Ring of Principal Ideals by Common Row and Separate Column Transformations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 6, June 1997, pp. 860–862, https://umj.imath.kiev.ua/index.php/umj/article/view/5074.
Section
Short communications