An inverse matrix of an upper triangular matrix can be lower triangular

Waldemar Hołubowski

Discussiones Mathematicae - General Algebra and Applications (2002)

  • Volume: 22, Issue: 2, page 161-166
  • ISSN: 1509-9415

Abstract

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In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.

How to cite

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Waldemar Hołubowski. "An inverse matrix of an upper triangular matrix can be lower triangular." Discussiones Mathematicae - General Algebra and Applications 22.2 (2002): 161-166. <http://eudml.org/doc/287665>.

@article{WaldemarHołubowski2002,
abstract = {In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.},
author = {Waldemar Hołubowski},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {upper tringular invertible matrix; group of matrices; Dedekind-finite ring; invertible matrix; upper triangular matrices; commutative ring; Dedekind finite ring},
language = {eng},
number = {2},
pages = {161-166},
title = {An inverse matrix of an upper triangular matrix can be lower triangular},
url = {http://eudml.org/doc/287665},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Waldemar Hołubowski
TI - An inverse matrix of an upper triangular matrix can be lower triangular
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 2
SP - 161
EP - 166
AB - In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.
LA - eng
KW - upper tringular invertible matrix; group of matrices; Dedekind-finite ring; invertible matrix; upper triangular matrices; commutative ring; Dedekind finite ring
UR - http://eudml.org/doc/287665
ER -

References

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  1. [1] H. Anton and C. Rorres, Elementary Linear algebra. Applications version, 8-th edition, J. Wiley, New York 2000. 
  2. [2] C.M. Bang, A condition for two matrices to be inverses of each other, Amer. Math. Monthly (1974), 764-767. Zbl0293.15004
  3. [3] I.D. Ion and M. Constantinescu, Sur les anneaux Dedekind-finis, Italian J. Pure Appl. Math. 7 (2000), 19-25. Zbl0971.16016
  4. [4] N. Jacobson, Structure of rings, Amer. Math. Soc., RI, Providence 1956. 
  5. [5] M.I. Kargapolov and Yu. I. Merzlakov, Fundamentals of the theory of groups, Springer-Verlag, New York 1979. 
  6. [6] D.J.S. Robinson, A course in the theory of groups, Springer-Verlag, New York 1982. Zbl0483.20001
  7. [7] A. Stepanov and N. Vavilov, Decomposition of transvections: a theme with variations, K- Theory 19 (2000), 109-153. Zbl0944.20031

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