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Rank formulas for certain products of matrices

โœ Scribed by Rudolf Ahlswede; Ning Cai

Publisher
Springer
Year
1993
Tongue
English
Weight
362 KB
Volume
4
Category
Article
ISSN
0938-1279

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We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices A โŠ— B, and in particular the Kronecker product of Fourier matrices We show how in the latter case, maximal rank-deficient submatrices can be constructed as tilings of rank-one blocks. Several such tilings

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Let V be a vector space of dimension n โ‰ฅ 3 over GF(2). We are concerned with the incidence of k-dimensional subspaces in (k + 2)-dimensional subspaces where 1 โ‰ค k โ‰ค n -2. We compute here an upper bound for the rank of the associated incidence matrices over GF(2).