Let $K$ be a field with a characteristic, other than 2. Let $V$ be a finite dimensional vector space over $K$, and let $\gamma: V \times V \to K$ be a bilinear form.
I now want to show that there exist unique bilinear forms $\gamma_s, \gamma_a: V \times V \to K$ that satisfy the following properties:
1) $\gamma_s$ is symmetric.
2) $\gamma_a$ is antisymmetric.
3) $\gamma = \gamma_s + \gamma_a$.
Thanks in advance. I'm not very used to working with bilinear forms.