I am going through an older linear algebra text ("Linear Algebra and Matrix Theory" by Nering) and in the section of the book on Hermitian forms, he asks the reader to show a specific function is a complex bilinear form. Try as I might, I can't find a definition for this term in the book. He does define a conjugate bilinear form (as a bilinear form linear in the second argument and conjugate linear in the first argument), and I think this is what he means by complex bilinear form, but I am wondering if anyone can clarify this point for me.
Thanks, Matt