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In page Linear subspace:

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In spaces with other bilinear forms, some but not all of these results still hold. In pseudo-Euclidean spaces and symplectic vector spaces, for example, orthogonal complements exist. However, these spaces may have null vectors that are orthogonal to themselves, and consequently there exist subspaces N {\displaystyle N} such that N ∩ N ⊥ ≠ { 0 } {\displaystyle N\cap N^{\perp }\neq \{0\}} . As a result, this operation does not turn the lattice of subspaces into a Boolean algebra (nor a Heyting algebra).[citation needed]