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A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.

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Is there an easy way to compute the maximum isotropic subspace over finite fields?

Given a quadratic form (or a symmetric $n \times n$ matrix $A$), an isotropic subspace is a subspace $U$ such that $$U^t A U=0,$$ If I am not mistaken, when the matrix is over reals, the maximum dime …
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