Eigenvectors and Eigenvalues The eigenvectors and values of a square matrix satisfy the equation AXEnX If a is symmetric and positive definite(covariance matrix) then all the eigenvectors are orthogonal and all the eigenvalues are positive independent components made up of the into Any covariance matrix can be broken doy eigenvectors and variances given by eigenvalues One method of generating samples of any random process(ie, generate white noise samples with variances given by eigenvalues, and transform using a matrix made up of columns of eigenvectors 03/1802 12.540Lec1203/18/02 12.540 Lec 12 4 Eigenvectors and Eigenvalues • The eigenvectors and values of a square matrix satisfy the equation Ax = λ x • If A is symmetric and positive definite (covariance matrix) then all the eigenvectors are orthogonal and all the eigenvalues are positive. • Any covariance matrix can be broken down into independent components made up of the eigenvectors and variances given by eigenvalues. One method of generating samples of any random process (ie., generate white noise samples with variances given by eigenvalues, and transform using a matrix made up of columns of eigenvectors