Let Sn be a covariance matrix satisfying the hypotheses of Theorem 8.6. To prove Theorem 8.7, proceed

Question:

Let Sn be a covariance matrix satisfying the hypotheses of Theorem 8.6. To prove Theorem 8.7, proceed as follows:
(a) Show that the trace of Sn is the total variance. (See Section 1.3, Exercise 43, for the definition of trace.)
(b) Show that there exists an orthogonal matrix P such that PTSnP = D, a diagonal matrix.
(c) Show that the trace of Sn is equal to the trace of D.
(d) Complete the proof?