LINEAR PRESERVERS OF BALANCED SINGULAR INERTIA CLASSES

Let S(n) denote the real symmetric n x n matrices and H(n) the real ve ctor space of n x n hermitian matrices. For 1 less than or equal to r less than or equal to n/2, let G(r, r, n - 2r) be the inertia class of all matrices in S(n) (in H(n)) with exactly r positive, r negative, a nd n - 2r zero eigenvalues. If T is a linear transformation on S(n) (o n H(n)) such that T maps G(r, r, n - 2r) into itself, we classify T pr ovided that n greater than or equal to 5r.