Let T and U be a self-adjoint linear operators on an n-dimensional inner product space V, and let A = [T]3, where 3 is an orthonormal basis for V. Prove the following results. (a) T is positive definite [semidefinite] if and only if all of its eigenval- ues are positive [nonnegative]. (b) T is positive definite if and only if Σ Aijajāį > 0 for all nonzero n-tuples (a₁, a2, ..., an). i.i

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