On Hermitian positive definite solution of the matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q\)
It is proved that the nonlinear matrix equation \(X-\sum _{i=1}^mA_i^*X^r A_i = Q(-1\leq r < 0\) or \(0< r<1)\) always has a unique Hermitian positive definite solution. Some bounds of the unique Hermitian positive definite solution are also given.
scientific article; zbMATH DE number 5564241