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

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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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[1] You Hong,Zheng Bao-dong.The elements of the special linear group SLn(F)as products of commutators of transvections. Advances in Mathematics . 2001
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