Oct 28, 2013 · Abstract:Say that A is a Hadamard factorization of the identity I_n of size n if the entrywise product of A and the transpose of A is I_n.
An n × n matrix M is called a fooling-set matrix of size n if its diagonal entries are nonzero and M k , ℓ M ℓ , k = 0 for every k ≠ ℓ .
The method of fooling sets refines arguments based on rectangle size. Intuitively, a fooling set is a set of inputs which is hard to cover by disjoint ...
Aug 14, 2012 · Abstract:An n\times n matrix M is called a \textit{fooling-set matrix of size n} if its diagonal entries are nonzero and M_{k,\ell} M_{\ell ...
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What is a fooling set?
Rank and fooling set size · The (Minimum) Rank of Typical Fooling-Set Matrices · Ordered biclique partitions and communication complexity problems · DENSITY AND ...
An n × n matrix M is called a fooling-set matrix of size n, if its diagonal entries are nonzero, whereas for every k ≠ ℓ we have M k,ℓ M ℓ,k = 0.
We settle this question. In characteristic zero, we construct an infinite family of rational fooling-set matrices with size $n = \binom{\mbox{rk} M+1}{2}$. In ...
Lemma 4. If f has a fooling set S of size t, then D(f) ≥ log2 t. 1.2 The Rank Lower Bound Method.
Jan 15, 2014 · SOME REMARKS ON THE IMPORTANCE OF FOOLING-SET MATRICES. While the fooling-set size vs. rank problem is of interest in its own right as a minimum ...
An n×n matrix M over some field K is called a fooling-set matrix of size n if its diagonal entries are all nonzero, but for all k 6= `, we have Mk,` M`,k�...