Degenerate Matrices Prof. Peter Lax, Courant Institute, New York, USA

Let A, B, and C be real, symmetric matrices of order n×n. If n is of the form 4k+2, k=1,2,..., then there is a nontrivial linear combination of A, B, C that is degenerate. This result is connected to the formation of singularities of solutions of PDE-s; it is also related to the representation of the discriminant as a sum of squares.