Speaker: Siddharth Mulherkar, ASP, Department of Mathematics, Ashoka University
Abstract: For any two Hermitian matrices $A,B$, we shall say that $A \leq B$ if $B-A$ is positive semi-definite. Note that $\leq$ is a partial order on the space of positive definite matrices. For any interval I \subseteq \R we say that $f:I \rightarrow \R$ is \matrix monotone of order $n$ if for all $n \times n$ Hermitian matrices $A,B$ we have $f(A) \geq f(B)$ whenever $A \geq B$ and $\sigma(A) \cup \sigma(B) \subset I$. If $f$ is matrix monotone for all $n$ then we say that $f$ is matrix monotone or operator monotone. We give various characterizations of operator monotone functions and outline some applications to matrix inequalities. This talk will be expository in nature.
6th April 2021
04:30 to 05:30 pm
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Online
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