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A determinantal inequality involving the Moore-Penrose inverse
Authors:J.L. Lavoie
Affiliation:Département de mathématiques Université Laval Québec, Québec Canada, G1K 7P4
Abstract:Let A be a rectangular matrix of complex numbers whose rows are partitioned into r arbitrary blocks:
/></figure> The Moore-Penrose inverses of each of these blocks are used to form the matrix <em>B</em> = (<em>A</em><sub>1</sub><sup>+</sup>,…, <em>A</em><sub><em>r</em></sub><sup>+</sup>). It is shown that 0 ? det (<em>AB</em>) ? 1. This is a generalized version of Hadamard's inequality.</td>
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