Metric spaces are sets on which you can measure the "distance" between any two points. The distance measurement is generally required to be symmetric (so distance from $A$ to $B$ is the same as distance from $B$ to $A$), positive for two distinct points, and obeying the triangle inequality.

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On visualizing the spaces $\Bbb{S}_{++}^n$ and $\Bbb{R}^n\times\Bbb{S}_{++}^n$ for $n=1,2,\ldots$

Let $\Bbb{S}_{++}^n$ denote the space of symmetric positive-definite $n\times n$ real matrices. I am looking for hints concerning the visualization of such spaces for $n=1,2,\ldots$. I know that ...