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arXiv · 1410.5140

Extension of a result of Haynsworth and Hartfiel

Minghua Lin
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Abstract

About last 70s, Haynsworth [6] used a result of the Schur complement to refine a determinant inequality for positive definite matrices. Haynsworth's result was improved by Hartfiel [5]. We extend their result to a larger class of matrices, namely, matrices whose numerical range is contained in a sector. Our proof relies on a number of new relations for the Schur complement of this class of matrices.

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Minghua Lin. 2014-10-20. Extension of a result of Haynsworth and Hartfiel. https://arxiv.org/abs/1410.5140

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