I want to see what the unit nuclear norm ball looks like.
So I think of matrices whose singular values add up to $1$. For simplicity, let's talk about symmetric, $2\times 2$ matrices (so that I can limit myself to $3$ dimensions). These matrices can be thought of as points in a $3$-dimensional space, and the coordinate values tell us about the entries in the matrix. But what shape will the matrices that have nuclear norm $1$ form?
I have seen figures showing it to be like a solid cylinder, but I can't see why.