What does it mean for a symmetric bilinear form over a finite field to be definite? Most sources (e.g. Wikipedia) only define definiteness for a form over $\mathbb{R}$ or $\mathbb{C}$. Yet I have seen references to definiteness over finite fields, but I can't find a proper definition.
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$\begingroup$I eventually found an answer in Lang's Algebra (Revised Third Ed., pg. 593): A symmetric form $b$ is definite if there is no $x\neq 0$ such that $b(x,x)=0$.
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