Positive, definite matrix symmetric

[kalish]

Under which conditions is a real positive definite matrix symmetric?

I have crossposted here: matrices - Positive definite matrix, symmetric? - Mathematics Stack Exchange

 

[Ackbach]

As the comments on M.SE indicate, positive-definiteness and symmetry are independent properties. Therefore, I would just go back to the definition: $A=A^{T}$ for symmetry. If you have complex-valued matrices, then perhaps the Hermitian property is more appropriate: $A=A^{\dagger}$.