is some of matrice with it's transpose positive definite? when eigenvalues of matrix is positive

Question

Suppose M = A+ A^T , and we know that all of eigenvalues of A are real and positive, is M positive definite? or semi positive definite?

Are all entries of $A$ real? – Ben Grossmann May 20 '14 at 00:17 — Ben Grossmann, May 20 '14 at 00:17
yes all of the elements are real – Alireza May 20 '14 at 00:31 — Alireza, May 20 '14 at 00:31
@Omnomnomnom do you have sth in mind? – Alireza May 20 '14 at 00:47 — Alireza, May 20 '14 at 00:47

score 4 · Answer 1 · answered May 20 '14 at 01:22

4

Consider $$ A = \begin{pmatrix} 1 &-4\\ 0 &1 \end{pmatrix}. $$ Then all of eigenvalues of $A$ are real and positive, but $M$ is indefinite.

answered May 20 '14 at 01:22

BARK

1 Answers1