# Definition of “Complex Bilinear Form”

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

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Most likely "complex bilinear form" here just means a bilinear form on a complex vector space. That is, it is linear in each argument, rather than linear in one argument and conjugate-linear in the other. –  Brad Nov 1 '12 at 4:00