LINEAR-MAPS WHICH PRESERVE A BALANCED NONSINGULAR INERTIA CLASS

Let n be an even integer such that n ≥ 4. Let T be an invertible linear map on the space of n × n real symmetric matrices which maps the set of matrices having inertia( n 2, n 2, 0) into itself. Then there exist a nonsingular matrix S and ε{lunate} = ± 1 such that T(A) = ε{lunate}StAS. This is an analogue of a result obtained for Hermitian matrices by Pierce and Rodman. © 1990.