Real symmetric matrices with multiple eigenvalues

10 October 2002
Prof Beresford Parlett
We describe "avoidance of crossing" and its explanation by von Neumann and Wigner. We show Lax's criterion for degeneracy and then discover matrices whose determinants give the discriminant of the given 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 discuss the 3 x 3 case in detail.
  • Computational Mathematics and Applications Seminar