2.20 ( ) www A positive definite matrix can be defined as one for which the quadratic form aTa (2.285) is positive for any

2.20 ( ) www A positive definite matrix Σ can be defined as one for which the quadratic form aTΣa (2.285)

is positive for any real value of the vector

a. Show that a necessary and sufficient condition for Σ to be positive definite is that all of the eigenvalues λi of Σ, defined by (2.45), are positive.