I was reading a text book, and encountered the following matrix: $H = h[e_r(\Omega_{r1})$ $e_r(\Omega_{r2}]$. Where, $e_{r}(\Omega_{rk})$ is a colomn vector with entries as $e^{-j2\pi k\Omega_{rk}}$. And it was written that the Matrix is a full rank matrix if $|e_r^*(\Omega_{r1}).e_r(\Omega_{r2})| \neq 1$.(* is the Hermitian operator)
How do we see the rank of a complex matrix? The expression appears to show that the given vectors are orthogonal. Are the matrices with non-orthogonal components always full rank?