• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.121-127
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• 1999

We can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.

• 충청수학회지
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• 제36권2호
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• pp.65-76
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• 2023

With the Stirling matrix S of the second kind and the Pascal matrix T, we study recurrence rules and sequences of certain sums over the matrix ST^k. We find a matrix E satisfying ST = ES and interrelations of S and the Stirling matrix of the first kind.

• 대한수학회지
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• 제48권1호
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• pp.33-48
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• 2011

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.