Extension of a result of Haynsworth and Hartfiel
Minghua Lin
TL;DR
This paper extends a classical determinant inequality for positive definite matrices to matrices with numerical range in a sector, using new Schur complement relations.
Contribution
It generalizes Haynsworth and Hartfiel's results to a broader class of matrices with sectorial numerical range.
Findings
Extended determinant inequality to sectorial matrices
Developed new relations for Schur complements in this class
Provided a broader framework for matrix inequalities
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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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Point processes and geometric inequalities