Involutions and semiinvolutions

Hiroyuki Ishibashi

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 533-541
  • ISSN: 0011-4642

Abstract

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We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.

How to cite

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Ishibashi, Hiroyuki. "Involutions and semiinvolutions." Czechoslovak Mathematical Journal 56.2 (2006): 533-541. <http://eudml.org/doc/31046>.

@article{Ishibashi2006,
abstract = {We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.},
author = {Ishibashi, Hiroyuki},
journal = {Czechoslovak Mathematical Journal},
keywords = {classical groups; vector spaces and linear maps; involutions; factorization of a linear map into a product of simple ones; classical groups; vector spaces; linear maps; involutions},
language = {eng},
number = {2},
pages = {533-541},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Involutions and semiinvolutions},
url = {http://eudml.org/doc/31046},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Ishibashi, Hiroyuki
TI - Involutions and semiinvolutions
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 533
EP - 541
AB - We define a linear map called a semiinvolution as a generalization of an involution, and show that any nilpotent linear endomorphism is a product of an involution and a semiinvolution. We also give a new proof for Djocović’s theorem on a product of two involutions.
LA - eng
KW - classical groups; vector spaces and linear maps; involutions; factorization of a linear map into a product of simple ones; classical groups; vector spaces; linear maps; involutions
UR - http://eudml.org/doc/31046
ER -

References

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  10. Products of matrices, In: Generators and Relations in Groups and Geometries. Proc. NATO ASI  (C), A.  Barlotti et al. (eds.), Kluwer Academic, Dordrecht-London, 1991, pp. 95–123. (1991) Zbl0729.15012MR1206912
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