Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - December 1973 - Volume 18, Issue 04  

Research Article

On identities associated with a discriminant

M. J. Newella1

a1 University College, Galway, Ireland

If the elements of a symmetric matrix lie in the real field it is well known that the roots of its characteristic equation are real. This implies that the discriminant of that equation (i.e. the product of the squared differences of the roots) is a polynomial in the elements which is non-negative and the same must be true for the leading coefficients of all the other Sturm functions associated with the characteristic equation. One would expect that it should be possible to express them as a sum of squares. Conversely, such an expression would establish the reality of the roots.

(Received April 26 1972)

(Revised October 22 1972)