 Cumulative coherence

For unit Euclidean norm columns, cumulative coherence measures the largest sum of $k$ correlations with one other column. Its domain is $0\le k\le N-1$, with ${\mu }_1(0)=0$ by the empty-sum convention. It is nondecreasing, ${\mu }_1(1)=\mu$ for $N\ge 2$, and ${\mu }_1(k)\le k\mu$, where $\mu$ is the mutual coherence. Keeping a sum of actual correlations can be substantially sharper than replacing each summand by the largest one.