Rigidity of a simple extended lower triangular matrix
For the all-ones lower triangular matrices, the upper and lower hounds on rigidity are known to match [P. Pudlak, Z. Vavrin, Computation of rigidity of order n(2)/r for one simple matrix, Comment Math. Univ. Carolin. 32 (2) (1991) 213-218]. In this short note, we apply these techniques to the all-ones extended lower triangular matrices, to obtain upper and lower bounds with a small gap between the two; we show that the rigidity is theta(n(2)/r). (C) 2008 Elsevier B.V. All rights reserved.
combinatorial problems computational complexity matrix rank