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.

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- October 23rd 2009, 03:19 AMgarymarkhovquadratic form and its eigenvalues
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. - October 23rd 2009, 06:23 AMHallsofIvy
Let be an eigenvalue of A and let x be an non-zero eigenvector corresponding to . What is ?

- October 23rd 2009, 09:58 AMtonio