Given a set of 3 dimensional points, the following covariance matrix was obtained c (3 by 3 matrix) =[ 1 2 1, 6 -1 0, -1, -2, -1]. In addition to the covariance matrix, three of its eigen vectors were also found: ev1= [ 1 6 -13] ev2=[-1 2 1] ev3= [2 3 -2]. Please ignore the fact that C is not a real covariance matrix as covariance matrix is always symmetric. Moreover the eigenvectors are also not orthogonal since eigenvectors are only perpendicular (orthogonal) to each other if the underlying matrix is symmetric. This example is created only so that the numbers are all integers and easy to work within a test environment. Project P1 onto the first (most important) principal component. P1 = [1 1 1]