Model families of quadratic forms.
Let [unk] be the subinterval of R of values sigma </= gamma. Let there be given a family F of real valued symmetric quadratic forms [Formula: see text] in real variables z(1),...,z(mu). If for fixed sigma[unk][unk] a nonnull mu-tuple z is a critical point of Q(sigma), sigma will be called a characteristic root of F. When F satisfies Conditions I, II, and III below, the index of Q(sigma) is the "count" of characteristic roots of F less than sigma.
Morse
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Institute for Advanced Study, Princeton, N.J. 08540.