I've been working on convex optimization and got stuck.
What exactly does a positive definite(p.d) matrix represent geometrically ? what kind of vector space it forms ?
If I have a p.d matrix which represent a convex cone (which I can't understand why), how do I prove the convexity for that matrix ? What's the input variable say X should be ?
Say if I have a plane, $$W^TX = B$$
at least I know I should put X into the equation, but for a p.d matrix...
it's just a matrix, why does that even represent a function ?
I am totally confused. Any hint helps a lot.