Consider the vector yi = (yi1, . . . , yip) 0 , whose sample mean is y = 0, and sample variance-covariance matrix is S. Denote the first principal component of y as ci = w 0yi with corresponding eigenvalue > 0. Denote the second principal component as bci = wb 0yi with corresponding eigenvalue >b 0. Use this information to answer the following questions:

d) Consider a second vector xi = Pyi , where P is an orthogonal matrix. Using the formula from the eigenvalue problem, provide expressions for two principal components of x. Hint: At some point, you must utilize the two eigenvectors already provided for S