On equivalence of pairs of matrices, which determinants are primes powers, over quadratic Euclidean rings

  • N.B. Ladzoryshyn Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
Keywords: quadratic Euclidean ring, equivalence of pairs of matrices
Published online: 2013-06-20

Abstract


We establish that a pair of matrices, which determinants are primes powers, can  be reduced over quadratic Euclidean ring $\mathbb{K}=\mathbb{Z}[\sqrt{k}]$ to their triangular forms with invariant factors on a main diagonal by using the common transformation of rows over a ring of rational integers $\mathbb{Z}$ and separate transformations of columns over a quadratic ring $\mathbb{K}$.

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How to Cite
(1)
Ladzoryshyn N. On Equivalence of Pairs of Matrices, Which Determinants Are Primes Powers, over Quadratic Euclidean Rings. Carpathian Math. Publ. 2013, 5 (1), 63-69.

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