Minimum rank of complements of Kneser graphs

We determine the symmetric minimum rank of the complement of the Kneser graph $\mathrm{KG}(n,k)$ over every infinite field. More precisely, if $I(n,k)$ is the graph on the $k$-subsets of $[n]$ in which two vertices are adjacent exactly when they intersect, then $${\mathrm{mr}}^{\mathbb{F}}(I(n,k))=n-2k+2$$ for every infinite field $\mathbb{F}$ and all integers $n,k$ with $2\le k\le n\mathrm{/}2$. In particular, over the real numbers, this settles a question posed in the AIM workshop open questions report on spectra of families of matrices described by graphs.