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I know that the dimension of the manifold formed by n-dimensional symmetric matrices is $\dfrac {n(n+1)}2$.But the manifold formed by n-dimensional positive definite symmetric matrices is of what dimension?Thanks!

Skdmg
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甄博涛
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    This can be answered by answering the following question: Given a positive definite symmetric matrix $A$ and a neighborhood of $A$ in the space of symmetric matrices, which matrices in the neighborhood are also positive definite? I suggest first looking at the case where $A = I$. – Deane Mar 31 '24 at 14:52

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