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Difference between revisions of "Unimodular matrix"

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A square matrix with determinant <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095370/u0953701.png" />. Sometimes when considering matrices over a commutative ring one understands by a unimodular matrix an invertible matrix.
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$#C+1 = 2 : ~/encyclopedia/old_files/data/U095/U.0905370 Unimodular matrix
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A square matrix with determinant  $  \pm  1 $.
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Sometimes when considering matrices over a commutative ring one understands by a unimodular matrix an invertible matrix.
  
 
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Often also a unimodular matrix is meant to have determinant <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095370/u0953702.png" />. The unimodular matrices, in any of the meanings, form a group under multiplication. Cf. also [[Unimodular transformation|Unimodular transformation]].
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Often also a unimodular matrix is meant to have determinant $  1 $.  
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The unimodular matrices, in any of the meanings, form a group under multiplication. Cf. also [[Unimodular transformation|Unimodular transformation]].

Latest revision as of 08:27, 6 June 2020


A square matrix with determinant $ \pm 1 $. Sometimes when considering matrices over a commutative ring one understands by a unimodular matrix an invertible matrix.

Comments

Often also a unimodular matrix is meant to have determinant $ 1 $. The unimodular matrices, in any of the meanings, form a group under multiplication. Cf. also Unimodular transformation.

How to Cite This Entry:
Unimodular matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Unimodular_matrix&oldid=49079
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article