Moore-Penrose inverse of set inclusion matrices

Bapat, R. B. (2000) Moore-Penrose inverse of set inclusion matrices Linear Algebra and its Applications, 318 (1-3). pp. 35-44. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0024-3795(00)00123-3

Abstract

Given integers s,k and v, let Wsk be the (vs) × (vs) 0-1 matrix, the rows and the columns of which are indexed by the s-subsets and the k-subsets of a v-set respectively, and where the entry in row S and column U is 1 if S⊂U and 0 otherwise. A formula for the Moore-Penrose inverse of Wsk over the reals is obtained. A necessary and sufficient condition for Wsk to admit a Moore-Penrose inverse over the set of integers modulo a prime p is given, together with a formula for the Moore-Penrose inverse when it exists.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Set Inclusion Matrix; Moore-Penrose Inverse; Incidence Matrix; Finite Field
ID Code:78327
Deposited On:19 Jan 2012 06:32
Last Modified:19 Jan 2012 06:32

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