MHB Positive, definite matrix symmetric

kalish1
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Under which conditions is a real positive definite matrix symmetric?

I have crossposted here: http://math.stackexchange.com/questions/661102/positive-definite-matrix-symmetric
 
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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: $A=A^{\dagger}$.
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...
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