Unformatted text preview: M is symmetric ( M = M ). • Prove that the eigenvectors x 1 ,..., x n corresponding to λ 1 ,...,λ n are orthogonal. Hint: consider x i M x jx j M x i . • Show that λ 1 = max z :  z  =1 z M z and λ 2 = max z :  z  =1 z x 1 =0 z M z . Hint: since there are n orthogonal eigenvectors, we can normalize these to ﬁnd an orthonormal basis of eigenvectors. Start by writing z as a linear combination of these basis elements. • Comment on the relevance of these observations to equation (3.49) and the surrounding discussion in HTF. Extra Credit: HTF 3.30 1...
View
Full
Document
This note was uploaded on 07/14/2010 for the course STAT 132 taught by Professor Haulk during the Spring '10 term at UBC.
 Spring '10
 Haulk
 Statistics

Click to edit the document details