# Math Help - Eigenvectors of positive definite matrix

1. ## Eigenvectors of positive definite matrix

Are the eigenvectors of positive definite matrix have all positive coordinates?

2. I know that eigenvalues of positive definite matrix are real positive. It does not say about eigenvectors. I

3. Oops, sorry. I misread your OP. I wouldn't think the components of an EV of a positive-definite matrix would have to be all positive. In fact, any non-zero scalar multiple of an eigenvector is an eigenvector. Hence, if all the components do happen to be positive, just multiply by a negative scalar, and you've got negative components.

4. Originally Posted by krystoferivanov
Are the eigenvectors of positive definite matrix have all positive coordinates?
Counterexample

$\begin{bmatrix}{1}&{0}\\{0}&{1}\end{bmatrix}\begin {bmatrix}{-1}\\{-1}\end{bmatrix}=1\begin{bmatrix}{-1}\\{-1}\end{bmatrix}$

Fernando Revilla

Edited: Sorry, I didn' see Ackbeet's post.