On Matricial Ranges of Some Matrices

one of the most well know concept in study of operator algebras is the notion of numerical range of an operator. Let (H , ·, ·) be a Hilbert space and let B(H ) be the C∗-algebra of all bounded linear operators on H with the identity operator I. When H has finite dimension n, we identify B(H ) with the algebra Mn := Mn(C) of all n × n complex matrices and In denotes the n × n identity matrix. The numerical range of an operator T ∈ B(H ) is defined by W (T ) = {T x, x; x ∈ H , x = 1}