A Pythagorean theorem for partitioned matrices

Jean-Christophe Bourin (1) , Eun-Young Lee

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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. For instance, if the matrix A is partitioned into three blocks A, B, C, then

Mots clés: Partitioned matrices; functional calculus; matrix inequalities 2010 mathematics subject classification. 15A18; 15A60; 47A30

Domaines: Analyse fonctionnelle [math.FA]

Jean-Christophe Bourin, Eun-Young Lee. A Pythagorean theorem for partitioned matrices. Proceedings of the American Mathematical Society, In press. ⟨hal-03526805⟩