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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 |
Description
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.