The question is: Consider the quadratic form where A is a k x k matrix and x is a k x 1 vector. Show that if A is positive definite, then all its eigenvalues are positive.
The question is: Consider the quadratic form where A is a k x k matrix and x is a k x 1 vector. Show that if A is positive definite, then all its eigenvalues are positive.
Not sure where to start.
Let be an eigenvalue of and one of its corresponding eigenvectors, then: