Question

Problem 2: Given a collection of data { zNJS R" we define 1. The sample mean of the points is given by 2. The sample variance of the points is given by N 2 3. The covariance matrix of the points is given by Suppose that (N) S R is a collection of data points. Using Lagrange Multipliers, show that the unit vector w for which the set (i.N), where wy, has maximum variance is the normalized eigenvector of Cov(ia) corresponding to the largest eigenvalue. Hint: Your Lagrangian here will be of the form L. wrAw + λ(1w12-1) for some matrix A. Also, save yourself some time writing by letting

Answer 1

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