::title::Matrix Identities and Determinant Identities for Composite Functions
::author::1::Xinghua Wang
::author::2::Aimin Xu
::address::1::Department of Mathematics, Zhejiang University, Hangzhou 310027, China
::address::2::Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China
::email::xwang@zju.edu.cn, xuaimin1009@yahoo.com.cn
::receive::Received 2009-3-9 Accepted 2010-2-4
::online::Available online 2010-9-20
::DOI::10.4208/jcm.1004-m3067
::keywords::Bell polynomial, Composite function, Determinant identity, Divided difference, Matrix identity.
::ams::65D05, 05A10, 15A23, 15A15.
::abstract::
We present some matrix and determinant identities for the divided differences of the 
composite functions, which generalize the divided difference form of Fa\`{a} di 
Bruno's formula. Some recent published identities can be regarded as special cases 
of our results.