Computer-aided study of a problem in Hermitian matrix theory
Let A be an \(n\times n\) positive definite Hermitian matrix and let B be an \(n\times n\) nonnegative semidefinite Hermitian matrix. For \(n\geq 3\), there is a smallest real number \(t_ n>2\) such that if \(-2<t\leq t_ n\) then the solution X to the equation \(A^ 2X+XA^ 2+tAXA=B\) is nonnegative semidefinite Hermitian. The authors describe their use of REDUCE and MAPLE in showing that \(t_ 4=4\) and in obtaining bounds for \(t_ n\) when \(5\leq n\leq 8\).
scientific article; zbMATH DE number 4179561