Publication detail

Reduction of matrices over orders of imaginary quadratic field

KUREŠ, M. SKULA, L.

Czech title

Redukce matic nad řády imaginárních kvadratických těles

English title

Reduction of matrices over orders of imaginary quadratic field

Type

journal article - other

Language

en

Original abstract

A special decomposition (called the near standard form) of (1,2)-matrices over a ring is introduced and a method for a reduction of such matrices is explained. This can be applied for a detection of elementary second order matrices among invertible second order matrices. The tool is used in detail over orders of imaginary quadratic fields, where an algorithm, a number of properties and examples are presented.

Czech abstract

Je zaveden speciální rozklad (nazvaný téměř standardní tvar) (1,2)-matic nad okruhem a je vysvětlena metoda rozkladu takových matic. To je pak použito k detekci elementárních matic druhého řádu mezi invertibilními maticemi druhého řádu. Uvedený nástroj je detailně užit nad řády imaginárních kvadratických těles, kde je prezentován algoritmus, řada vlastností a příkladů.

English abstract

A special decomposition (called the near standard form) of (1,2)-matrices over a ring is introduced and a method for a reduction of such matrices is explained. This can be applied for a detection of elementary second order matrices among invertible second order matrices. The tool is used in detail over orders of imaginary quadratic fields, where an algorithm, a number of properties and examples are presented.

Keywords in Czech

Řád imaginárního kvadratického tělesa, normovaný okruh, zobecněný euklidovský okruh, invertibilní matice, elementární matice, (1,2)-matice

Keywords in English

Order of an imaginary quadratic field, Normed ring, Generalized Euclidean ring, Invertible matrix, Elementary matrix, (1,2)-Matrix

RIV year

2011

Released

10.06.2011

Publisher

Elsevier

ISSN

0024-3795

Journal

LINEAR ALGEBRA AND ITS APPLICATIONS

Volume

435

Number

6

Pages from–to

1903–1919

Pages count

17

BIBTEX


@article{BUT50911,
  author="Miroslav {Kureš} and Ladislav {Skula},
  title="Reduction of matrices over orders of imaginary quadratic field",
  journal="LINEAR ALGEBRA AND ITS APPLICATIONS",
  year="2011",
  volume="435",
  number="6",
  month="June",
  pages="1903--1919",
  publisher="Elsevier",
  issn="0024-3795"
}