Journal of Guangdong University of Technology ›› 2006, Vol. 23 ›› Issue (1): 127-133.

• Comprehensive Studies • Previous Articles     Next Articles

The Normalized Form of the Two Commutable Transvections under the Same Similarity

  

  1. (1.Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510006,China;2.School of Mathematical Sciences,Heilongjiang University,Ha’erbin 150080,China)
  • Online:2006-02-02 Published:2006-02-02

Abstract: Let F be a field,and n be a positive integer,GLn(F)denotes the General Linear Group of degree n over F.A matrix Ain GLn(F)is called a transvection if A is similar to T12(1) whose elements on(1,2)-position and principal diagonal are all 1 and 0 else.Let A and B be two transvections,a P∈GLn(F) exists,P-1AP=T12(1),P-1Bcan be denoted with four simple forms if A and Bare commutative.

Key words: transvection; centralizer; similitude; normalized form;

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