Some Notices on Mina Matrix and Allied Determinant Identities
Received:April 20, 2015  Revised:January 13, 2016
Key Word: Mina determinant identity   Mina matrix   LU factorization   derivative operator   inverse   combinatorial identity   Lagrange interpolation   Melzak's formula  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11401237).
Author NameAffiliation
Jin WANG Department of Mathematics, Soochow University, Jiangsu 215006, P. R. China 
Xinrong MA Department of Mathematics, Soochow University, Jiangsu 215006, P. R. China 
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Abstract:
      By means of a special LU factorization of the Mina matrix with the $n$-th row and $k$-th column entry $\mathbf{D}^{n}_x(f^{a_k}(x))$, we obtain not only a short proof of the Mina determinant identity but also the inverse of the Mina matrix. Finally, by use of some similar factorizations built on the Lagrange interpolation formula, two new determinant identities of Mina type are established.
Citation:
DOI:10.3770/j.issn:2095-2651.2016.03.001
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