3 May
2020
3 May
'20
12:42 p.m.
Yes, if A is symmetric, then A can be diagonalized with an orthogonal similarity matrix S. Then x^T A x = x^T (S^T D S) x = (Sx)^T D (Sx) > 0. -- Gene On Sunday, May 3, 2020, 11:22:57 AM PDT, Cris Moore via math-fun <math-fun@mailman.xmission.com> wrote: this holds if A is symmetric, right? the counterexample is not.
On May 3, 2020, at 12:16 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Then in reading Arthur Gelb, "Applied Optimal Estimation", I found problem 2-3, in which A is a matrix.
"Show that A is positive definite if and only if all of its eigenvalues are positive."
-- Gene
Cris Moore moore@santafe.edu