可交换平延在同时相似下的标准形

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

设F是域,n为正整数,GLn(F)表示域F上的n级一般线性群,T12(1)表示(1,2)位置元与所有对角元都是1而其余元为零的GLn(F)中元;GLn(F)中与T12(1)相似的矩阵称为F上的n级平延.A,B为两个平延,当A与B可交换时,P∈GLn(F),使P-1AP=T12(1),P-1BP可表为4种简单形式.

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^-1A=T12（1）, P^-1B can be denoted with four simple forms if A and B are commutative.