Question: Let V be a finite dimensional vector space over R with a positive definite scalar product and let A be symmetric linear operator on

Let V be a finite dimensional vector space over R with a positive definite scalar product and let A be symmetric linear operator on

Let V be a finite dimensional vector space over R with a positive definite scalar product and let A be symmetric linear operator on V. (a) State the Spectral Theorem for A. (b) Show that the eigenvalues of A are positive if and only if (Av, v) > 0, for all v 0.

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