J. Comp. Math., 28 (2010), pp. 929-938.

Matrix Identities and Determinant Identities for Composite Functions

Xinghua Wang 1, Aimin Xu 2

1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2 Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China

Received 2009-3-9 Accepted 2010-2-4
Available online 2010-9-20


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.

Key words: Bell polynomial, Composite function, Determinant identity, Divided difference, Matrix identity.

AMS subject classifications: 65D05, 05A10, 15A23, 15A15.

Email: xwang@zju.edu.cn, xuaimin1009@yahoo.com.cn

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