An Equality for Trace of Matrix over a Generalized Quaternion Algebra
Received:October 28, 2003  
Key Words: generalized quaternion algebra   matrix   similarity   trace.  
Fund Project:
Author NameAffiliation
CHENG Shi-zhen Dept. of Basic Sci.
Beijing Institute of Civil Engineering and Architecture
Beijing
China
School of Mathematical Sciences
Beijing Normal University
Beijing
China 
TIAN Yong-ge Dept. of Math. and Statistics
Queen's University Kingston
Ontario
Canada K7L 3N6 
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Abstract:
      The well-known trace equality of similar matrices does not necessarily hold for matrices over non-commutative algebras and rings. An interesting question is to give conditions such that trace equality of similar matrices holds for matrices over a non-commutative algebra or ring. In this note, we show that for any two matrices $A$ and $B$ over a generalized quaternion algebra defined on an arbitrary field ${\bf F}$ of characteristic not equal to two, if $A$ and $B$ are similar and the main diagonal elements of $A$ and $B$ are in $\bf F$, then their traces are equal.
Citation:
DOI:10.3770/j.issn:1000-341X.2006.01.009
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