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Weighted generalizations of Hoffman’s ratio bound on the independence number of a regular graph are surveyed.. Several known bounds are reviewed as special cases of

The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical

The first author is supported by a grant from Tianyuan Funds of China (10826065) and a grant from Youth Funds of Shanxi (2009021002); the second author is supported by a grant

Intelligence, Hebei University, Baoding (071002), China ([email protected], [email protected]). Supported by the Australian

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Reference [7] derives bounds on the condition number (through bounds on the singular values) of Vandermonde matrices with nodes on the unit circle, dependant on the minimum and

We propose bounds for the spectrum and invertibility conditions which in the finite case improve the Hadamard criterion for matrices that are ”close” to block triangular

In this paper we will study the spectral properties of Wigner real symmetric and Hermitian random matrices in the case when the matrix entries have heavy tails of distribution..