本文从Thurston的观点出发，用二阶逼近来定义与讨论矩阵空间C~(m×n)（m≤n）中的域上全纯映照的Schwarz导数及高阶Schwarz导数，证明：如果它们存在的话，那么它们是在R_I（m,n）的紧对偶空间CG（m，n）的全纯自同构群下的相似不变量．并证明：这样得到的Schwarz导数与前几文［1－4］中由Ahlfors的观点得到的Schwarz导数是相一致的．此外，还应用这种观点定义与讨论了C~N中的域上全纯映照的Schwarz导数．

From point view of Thurston we define and discuss the Schwarzian derivativeand Schwarzian derivative of high order of holomorphic mappings on domains of thematrix space Cm×n (m n) by using the approximation of second order. We provethat if the Schwarzian derivatives exist,then they are the invariant up to similarityunder the group of holomorphic auomophism of the compact dual space of RI(m,n)Also we prove that the Schwarzian in this paper is same as the Schwarzian in [1-4]Schwarzian of holomorphic mappings on domains of Cn