Normal operator

In functional analysis and linear algebra, a **normal operator** is a bounded linear operator \( T \) on a Hilbert space that commutes with its adjoint. Specifically, an operator \( T \) is said to be normal if it satisfies the condition: \[ T^* T = T T^* \] where \( T^* \) is the adjoint of \( T \). ### Key Properties of Normal Operators 1.