1- https://doi.org/10.1155/2010/241908
Trace-Inequalities and Matrix-Convex Functions
- Dec 2, 2009
- Fixed Point Theory and Applications
- Tsuyoshi Ando
Abstract
Abstract A real-valued continuous function "Equation missing" on an interval "Equation missing" gives rise to a map "Equation missing" via functional calculus from the convex set of "Equation missing" Hermitian matrices all of whose eigenvalues belong to the interval. Since the subpace of Hermitian matrices is provided with the order structure induced by the cone of positive semidefinite matrices, one can consider convexity of this map. We will characterize its convexity by the following trace-inequalities: "Equation missing" for "Equation missing". A related topic will be also discussed.
- # Cone Of Positive Semidefinite Matrices
- # Matrix-Convex Functions
- # Real-valued Continuous Function
- # Hermitian Matrices
- # Functional Calculus
- # Cone Of Matrices
- # Real-valued Function
- # Positive Matrices
- # Positive Semidefinite Matrices
- # Semidefinite Matrices
