Representations of Finite Groups
K. N. Srinivasa Rao · Texts and readings in physical sciences · 2006
Let G be a finite group of order h. We first recall that an operator α is said to be unitary with respect to a scalar product (x, y) if it satisfies the condition $$\left( {\alpha x,\alpha y} \right) = \left( {x,y} \right){\text{for all }}x,y$$ of Eq. (3.15.17) and that a unitary operator α is represented by a unitary matrix relative to a basis e which is orthonormal with respect to the given scalar product, as observed at the end of section (3.15).