Name for “effective rank”-type quantity?

Does the following quantity come up under any standard names in the literature?

$$f(A)=\frac{\text{tr}A}{\|A\|_2}$$

I'm tempted to call it "effective rank" because it can be used as a convex lower bound on rank (https://arxiv.org/pdf/0706.4138.pdf), but this name doesn't seem standard.