I was looking around different textbooks and websites for the definition of a Hermitian adjoint. All the resources that I have checked including the one I am studying at the moment (Jeevanjee's Intro. to Tensors and Group Theory for Physicists pg. 48 and footnote on pg. 120) assume a positive-definite non-degenerate Hermitian form to define a Hermitian adjoint. I was wondering if you can at all define a Hermitian adjoint when the Hermitian form is not positive definite, and if there is a problem with that what is it?