Let Sn be a covariance matrix satisfying the hypotheses of Theorem 8.6. To prove Theorem 8.7, proceed
Question:
(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?
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a The diagonal entries of S n are the sample variances for the nvariables and the total varianc...View the full answer
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
Question Posted:
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