A Pythagorean theorem for partitioned matrices
Jean-Christophe Bourin, Eun-Young Lee
TL;DR
This paper proves a Pythagorean theorem for partitioned matrices, leading to new operator inequalities that extend classical geometric concepts to matrix analysis.
Contribution
It introduces a novel Pythagorean theorem for matrix blocks, providing new insights and inequalities in operator theory.
Findings
Established a Pythagorean theorem for partitioned matrices
Derived new operator inequalities from the theorem
Extended geometric concepts to matrix analysis
Abstract
We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematical Inequalities and Applications · Mathematics and Applications