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Let V be an F-vector space (F $ = \mathbb{R}$ or $\mathbb{C}$)

My notes define a quadratic form as:

A map $q:V \rightarrow F$ s.t. $q(v)=\beta(v,v)$ for some (symmetric) bilinear form $\beta:V\times V \rightarrow F$.

Later on the notes define an Hermitian form $\gamma:V\times V \rightarrow F$ to be a conjugate-symmetric sesquilinear form. It then says that given an Hermitian form $\gamma,$ we can define a quadratic form $q:V \rightarrow F$ by $q(v)=\gamma(v,v).$

Does this fit with the definition of "quadratic form" given above - I'm quite confused?

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