Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 161-166
doi: 10.7151/dmgaa.1055

[BIBTex] [PDF] [PS]

AN INVERSE MATRIX OF AN UPPER TRIANGULAR MATRIX CAN BE LOWER TRIANGULAR

Waldemar Houbowski

Institute of Mathematics
Silesian University of Technology
Kaszubska 23, 44-101 Gliwice, Poland
e-mail: wholub@polsl.gliwice.pl

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.

Keywords: upper tringular invertible matrix, group of matrices, Dedekind-finite ring.

2000 Mathematics Subject Classification: 20H25.

References

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