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Extension of a result of Haynsworth and Hartfiel

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Abstract

Haynsworth (Proc Am Math Soc 24:512–516, 1970) used a result of the Schur complement to refine a determinant inequality for positive definite matrices. Haynsworth’s result was improved by Hartfiel (Proc Am Math Soc 41:463–465, 1973). We extend their results 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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    Minghua Lin

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Minghua Lin

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  1. Minghua Lin
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Correspondence to Minghua Lin.

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Lin, M. Extension of a result of Haynsworth and Hartfiel. Arch. Math. 104, 93–100 (2015). https://doi.org/10.1007/s00013-014-0717-2

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  • DOI: https://doi.org/10.1007/s00013-014-0717-2

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