# The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension

@inproceedings{Glasby2021ThePO, title={The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension}, author={Stephen P. Glasby and Alice C. Niemeyer and Cheryl E. Praeger}, year={2021} }

Let n, n be positive integers and let V be an (n+n)-dimensional vector space over a finite field F equipped with a non-degenerate alternating, hermitian or quadratic form. We estimate the proportion of pairs (U, U ), where U is a non-degenerate n-subspace and U ′ is a non-degenerate n-subspace of V , such that U +U ′ = V (usually such spaces U and U ′ are not perpendicular). The proportion is shown to be at least 1 − c/|F| for some constant c 6 2 in the symplectic or unitary cases, and c < 3 in…

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