Lower bounds for permanents of Gram matrices having a rank one principal submatrix

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

The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices

The paper mainly discusses the lower bounds for the rank of matrices and sufficient conditions for nonsingular matrices. We first present a new estimation for [Formula: see text] ([Formula: see text] is an eigenvalue of a matrix) by using the partitioned matrices. By using this estimation and inequality theory, the new and more accurate estimations for the lower bounds for the rank are deduced....

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...

Equations for Lower Bounds on Border Rank

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

An Inequality for Permanents of (0,1)-Matrices*

Let A be an n-square (0, 1)-matrix, let ri denote the i-th row sum of A, i = 1 ..... n, and let per(A) denote the permanent of A. Then per(A) ~< H ri q~/-2,.1 I + V T where equality can occur if and only if there exist permutation matrices P and Q such that PAQ is a direct sum of l-square and 2-square matrices all of whose entries are 1. I f A = (ai~) is an n-square mat r ix then the permanent ...