General Lower Bounds on Maximal Determinants of Binary Matrices

Probabilistic lower bounds on maximal determinants of binary matrices

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of the distance d to the nearest (smaller) Hadamard matrix, defined by d = n − h, where h is the order of a Hadamard matrix and h is maximal subject to h ≤ n. The lower bounds on R(n) ...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Lower bounds on maximal determinants of binary matrices via the probabilistic method

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n be the ratio of D(n) to the Hadamard upper bound. We give several new lower bounds on R(n) in terms of d, where n = h + d, h is the order of a Hadamard matrix, and h is maximal subject to h ≤ n. A relatively simple bound is R(n) ≥ ( 2 πe )d/2( 1− d ( π 2h )1/2) for all n ≥ 1. An asymptotically sharper bound is R(n) ≥...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...