I am reading Steele's Cauchy-Schwarz Master Class, and am wondering what "inversion preserving" refers to the following exercise from Chapter 1:
Exercise 1.6 (A Sum of Inversion Preserving Summands) Suppose that $p_k>0$ for $1\leq k\leq n$ and $\sum_{k=1}^np_k=1$. Show that $$\sum_{k=1}^n\left(p_k+\frac1{p_k}\right)^2\geq n^3+2n+\frac1n.$$
So, what "inversion" leaves the summands $(p + 1/p_k)^2$'s unchanged?