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An extension of the generalized pascal matrix and its algebraic properties

✍ Scribed by Zhizheng Zhang; Maixue Liu

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 198 KB
Volume: 271
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)00266-8

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✦ Synopsis

The extended generalized Pascal matrix can be represented in two different ways: as a lower triangular matrix d~n [x, y] or as a symmetric ~.[x, y]. These matrices generalize Pn[X], Qn[X], and Rn[X], which are defined by Zhang and by Call and Velleman. A product formula for dp.[ x, y] has been found which generalizes the result of Call and Velleman. It is shown that not only can ¢.[x, y] be factorized by special summation, but also ~[x, y] as pn[xy]~T[y, 1/x] or ¢n[x, y]pT[y/x]. Finally, the inverse of ~.[x, y] and the values of detdPn[x, y], detqb~-l[x, y], det ~[x, y], and det ~-l[x, y] are given.

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