Let V be a finite dimensional vector space over R with a positive definite scalar product...

Transcribed Image Text:

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. 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.

Answer rating: 100% (QA)

The detailed ... View the full answer