The standard form of matrices over the ring of Gaussian integers with respect to (z,k)-equivalence

Petrychkovych, V. М.; Zelisko, H. V.; Ladzoryshyn, N. B.

doi:10.15407/apmm2020.18.5-10

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Main Results Let K = Z[1

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2024

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Cited by 3 publications

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“…Proof. Proposition of the theorem, if the quadratic ring K is the ring of Gaussian integers Z[i] is proved in the article [17].…”

Section: Main Results Let K = Z[mentioning

confidence: 99%

The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence

Ladzoryshyn

Petrychkovych

2022

Mat. Stud.

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The $(z,k)$--equivalence of matrices over imaginary Euclideanquadratic rings is investigated. The classes of matrices overthese rings are selected for which the standard form with respectto $(z,k)$--equivalence is uniquely defined and equal to the Smithnormal form. It is established that the number of standard formsover imaginary Euclidean quadratic rings is finite. Bounds for anumber of standard forms are established.

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“…Proof. Proposition of the theorem, if the quadratic ring K is the ring of Gaussian integers Z[i] is proved in the article [17].…”

Section: Main Results Let K = Z[mentioning

confidence: 99%

The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence

Ladzoryshyn

Petrychkovych

2022

Mat. Stud.

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On Standard Forms of the Pairs of Matrices Over the Ring of Gaussian Integers with Respect to the (z,k)-Equivalence

Ladzoryshyn,

Petrychkovych

2024

J Math Sci

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On standard forms of pairs of matrices over the ring of Gaussian integers with respect to (z,k)-equivalence

Ladzoryshyn,

Petrychkovych

2021

Mat. Met. Fiz. Mekh. Polya

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The standard form of matrices over the ring of Gaussian integers with respect to (z,k)-equivalence

Cited by 3 publications

References 9 publications

The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence

The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence

On Standard Forms of the Pairs of Matrices Over the Ring of Gaussian Integers with Respect to the (z,k)-Equivalence

On standard forms of pairs of matrices over the ring of Gaussian integers with respect to (z,k)-equivalence

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