Can a positive semidefinite matrix be asymmetric?

[Kumar Shaurya Shankar]

Hi, 

I've been going around in circles for a long time on this (wrt Q3.2.1) , and I have conflicting answers as to this query.

http://math.stackexchange.com/questions/4336/if-eigenvalues-are-positive-is-the-matrix-positive-definite?rq=1

http://www.sciencedirect.com/science/article/pii/0024379579901228

So, I have examples of non symmetric matrices with positive eigen values that give me the required result. But is that expected/acceptable?

Thanks!

[Vagelis Papalexakis]

Hi!

I guess this is not right, since a positive semidefinite matrix is *defined* to be symmetric and (a whole list of equivalent statements, such as) having non-negative eigenvalues.

Hope that clarifies things a bit, at least.

Vagelis

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[Ishan Misra]

This might help:
http://en.wikipedia.org/wiki/Positive-definite_matrix#Quadratic_forms

In the case of real matrices -
"It turns out that the matrix M is positive definite if and only if it is symmetric and its quadratic form is a strictly convex function"

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Regards,

Ishan Misra

Masters in Robotics

Carnegie Mellon University

All our knowledge has its origins in our perceptions.

Work as if somewhere something is waiting to be discovered.

[Barnabas Poczos]

Exactly, a positive semidefinite matrix has to be symmetric by definition.
See, e.g. here:
http://en.wikipedia.org/wiki/Positive-definite_matrix

Barnabas

On Tue, Feb 19, 2013 at 10:27 PM, Vagelis Papalexakis
<vagelis.p...@gmail.com> wrote: