In
matrix notation let
A be some
matrix. The complex conjugate (c.c.) of
A is denoted
with a "*" i.e.
c.c.(A) defined A*.
You generate it by replacing each element of the matrix aij with its complex conjugate a*ij
In quantum mechanics wavefunctions
can be represented in matrix form.
The proabaility of a state is the integral over
space of the wavefunction multiplied by its c.c.
This gauranties a positive definite value for the
probability.
A real number is equal to it's complex conjugate.