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Multiple Eigenvalues

Colloquium

Speaker: Professor Peter Lax, Courant Institute, New York University
Location: 693 Kerr
Start time: Mon, Mar 5 2001, 4:10PM

I will present two results. i) Let A, B, and C be three nxn real symmetric matrices.If n is congruent 2(mod 4), then xA+yB+zC has a double eigenvalue for some nonzero value of x,y,z. This result is of interest in the theory of symmetric hyperbolic systems of PDE-s. ii) The discriminant of real, symmetric nxn matrices can be written as a sum of squares of homogeneous polynomials the entries of the matrix.