Real symmetric matrices with multiple eigenvalues
Beresford Parlett (Berkeley)
We describe "avoidance of crossing" and its explanantion by von Neumann and Wigner. We show Lax's criterion for degeneracy and discover matrices whose determinants give the discriminant of a given symmetric matrix. This yields a simple proof of the bound given by Ilyushechkin on the number of terms in the expansion of the discriminant as a sum of squares. We present the 3 X 3 case in detail.