Let S-n(F) denote the space of all n x n symmetric matrices over the field
F. Given a positive integer k such that k < n, let d(n, k, F) be the smalle
st integer l such that every l dimensional subspace of S-n(F) contains a no
nzero matrix whose rank is at most k. It is our purpose to consider d(n,k,F
) for F = R and F = C. While the computation of d(n, k, C) is quite straigh
tforward, we point out the difficulty in evaluating d(n, k, R). We obtain p
artial results regarding d(n, n-2, R), and in particular show that 4 less t
han or equal to d(4, 2, R) less than or equal to 5. (C) 1999 Elsevier Scien
ce Inc. All rights reserved.