摘要
设X、Y是任意n×n实矩阵,对于矩阵指数函数,一般说,e^X·e^Y≠e^(X+Y),除非〔X,Y)=0.当[x_1y]=(x+y)X-(x-y)Y时,本文通过浩繁的计算,终究得出一个具体的解析函数λ=f(x,y),使得e^X·e^Y=e^(X+Y+λ[X’Y])所得此公式,实际上正是一般线性群GL(n,R)的 2—Lie子群结构的一种表示.
Let gl(n, R)denote the Lie algebra of all real n×n matrices, the bracket being [X, Y]=XY-YX, X, Y∈gl(n, R), identified with the Lie aigebra of the general linear group Gl(n, R).In this paper, we prove the followingTheorem If X, Y∈gl(n, R)such that [X, Y] = (x+y)X-(x-y)Y, thenwhere the function f(x,y) defined by f(x,y)=
