The minimum size of a finite subspace partition

By Esmeralda Nastase, P. Sissokho. 2011

182 citations recorded by the source corpus.

Abstract A subspace partition of P = PG ( n , q ) is a collection of subspaces of P whose pairwise intersection is empty. Let σ q ( n , t ) denote the minimum size (i.e., minimum number of subspaces) in a subspace partition of P in which the largest subspace has dimension t. In this paper, we determine the value of σ q ( n , t ) for n ⩽ 2 t + 2 . Moreover, we use the value of σ q ( 2 t + 2 , t ) to find the minimum size of a maximal partial t-spread in PG ( 3 t + 2 , q ) .

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/7bd4e709a7d47fd00016ad831685159260e52f6d

Citations in the corpus

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• A generalized subspace approach for enhancing speech corrupted by colored noise (2003, unknown): “It can be shown [9] that such a matrix exists and can simultaneously diagonalize the two matrices in the following way: (12) where and are the eigenvalue matrix and eigenvector matrix respectively of , i.e., (13) It can be shown that is a real matrix [10], assuming that is positive definite.”
• Inference of gene regulatory networks and compound mode of action from time course gene expression profiles (2006, unknown): “We apply the PCA to reduce the dimension of Equation (5) by decomposing Y using singular value decomposition (Lay, 2002) X ¼ H V D T0‚ ð6Þ where columns V are left singular vectors, rows of T0 are right singular vectors and D is a diagonal matrix of singular values arranged in descending order.”
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