Explicit inverse of the Pascal matrix plus one
نویسندگان
چکیده
منابع مشابه
Explicit inverse of the Pascal matrix plus one
This paper presents a simple approach to invert the matrix P n + I n by applying the Euler polynomials and Bernoulli numbers, where P n is the Pascal matrix.
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Let L(n)p be the Pascal lower triangular matrix with coefficients `i j ́ (mod p), 0 ≤ i, j < n. In this paper, we found the inverse of L(n)p modulo p. In fact, we generalize a result due to David Callan [4].
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In this paper, we prove the q -analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations ∗q and ∗1/q , we obtain a q -analogue of the Riordan representation of the q -Pascal matrix. In addition, by aid of the q -Lagrange expansion formula we get q -Riordan representation for its inverse matrix.
متن کاملAn involutory Pascal matrix
An involutory upper triangular Pascal matrix Un is investigated. Eigenvectors of Un and of UT n are considered. A characterization of Un is obtained, and it is shown how the results can be extended to matrices over a commutative ring with unity. © 2004 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2006
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms/2006/90901