Add to ORKGLet f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We prove that if f is matrix-subadditive of ordern then it has the form f(t) = αt for some α ∈ ℝ. Moreover, we show that if the inequality Tr (f(A + B)) ≤ Tr(f(A)) + Tr (f (B)) holds true for every pair A, B of Hermitian positive semidefinite n × n-matrices then f is concave. © 1998 OPA (Overseas Publishers Association) Amsterdam B.V. Published under license under the Gordon and Breach Science Publishers imprint
In this note, the matrix trace inequality for positive semidefinite matrices A and B, is established...
There is growing interest in optimization problems with real symmetric matrices as variables. Genera...
AbstractWe review some recent convexity results for Hermitian matrices and we add a new one to the l...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
AbstractIn 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We e...
AbstractLet f(t) be a non-negative concave function on the positive half-line. Given an arbitrary pa...
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any m...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
AbstractIn this note, we consider some norm inequalities related to the Rotfel’d Trace InequalityTrf...
Abstract A real-valued continuous function on an interval gives rise to a map via functional c...
AbstractIn 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We e...
AbstractWe supply new proofs for two important properties of the matrix-concave function F(A) = (K′A...
AbstractWe supply new proofs for two important properties of the matrix-concave function F(A) = (K′A...
AbstractLet A and B be Hermitian matrices. We say that A⩾B if A−B is nonnegative definite. A functio...
In this note, the matrix trace inequality for positive semidefinite matrices A and B, is established...
There is growing interest in optimization problems with real symmetric matrices as variables. Genera...
AbstractWe review some recent convexity results for Hermitian matrices and we add a new one to the l...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
Let f be a real-valued function on [0, ∞) with f(0) = 0 and n be a natural number greater than 1. We...
AbstractIn 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We e...
AbstractLet f(t) be a non-negative concave function on the positive half-line. Given an arbitrary pa...
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any m...
A real-valued continuous function f(t) on an interval (α,β) gives rise to a map X!...
AbstractIn this note, we consider some norm inequalities related to the Rotfel’d Trace InequalityTrf...
Abstract A real-valued continuous function on an interval gives rise to a map via functional c...
AbstractIn 1999 Ando and Zhan proved a subadditivity inequality for operator concave functions. We e...
AbstractWe supply new proofs for two important properties of the matrix-concave function F(A) = (K′A...
AbstractWe supply new proofs for two important properties of the matrix-concave function F(A) = (K′A...
AbstractLet A and B be Hermitian matrices. We say that A⩾B if A−B is nonnegative definite. A functio...
In this note, the matrix trace inequality for positive semidefinite matrices A and B, is established...
There is growing interest in optimization problems with real symmetric matrices as variables. Genera...
AbstractWe review some recent convexity results for Hermitian matrices and we add a new one to the l...