Generalized equivalence of collections of matrices and common divisors of matrices

Vasyl' M. Petrychkovych

Geodesic

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Generalized equivalence of collections of matrices and common divisors of matrices

Vasyl' M. Petrychkovych

Algebra and discrete mathematics, no. 2 (2004), pp. 84-91.

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

The collections

(A_{1}, \dots, A_{k})

and

(B_{1}, \dots, B_{k})

of matrices over an adequate ring are called generalized equivalent if

A_{i} = U B_{i} V_{i}

for some invertible matrices

U

and

V_{i}, i = 1, \dots, k

. Some conditions are established under which the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described.

Keywords: generalized equivalence, canonical diagonal form, common divisors.
Mots-clés : collection of matrices

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     title = {Generalized equivalence of collections of matrices and common divisors of matrices},
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     pages = {84--91},
     publisher = {mathdoc},
     number = {2},
     year = {2004},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/ADM_2004_2_a8/}
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Vasyl' M. Petrychkovych. Generalized equivalence of collections of matrices and common divisors of matrices. Algebra and discrete mathematics, no. 2 (2004), pp. 84-91. https://geodesic-test.mathdoc.fr/item/ADM_2004_2_a8/