Analytic function of a matrix: Difference between revisions

Revision as of 14:35, 29 May 2020

Revision as of 08:15, 28 July 2020

Line 192:

===Examples===

The matrix log is both operator monotone and operator concave. The matrix square is operator convex. The matrix exponential is none of these. '''Loewner's Theoremtheorem''' states that a function on an ''open'' interval is operator monotone if and only if it has an analytic extension to the upper and lower complex half planes so that the upper half plane is mapped to itself.<ref name="Bhatia" />

==See also==