sqrtNcNv

sqrtNcNv is a compact, informal notation for the quantity sqrt(N_c N_v), where N_c and N_v denote nonnegative quantities such as counts or measurements. In standard notation, this value is written as sqrt(N_c N_v). The expression represents the geometric mean of N_c and N_v, since the geometric mean of two numbers a and b is sqrt(a b). The condition of nonnegativity ensures the result is real.

Properties include that for N_c ≥ 0 and N_v ≥ 0, sqrt(N_c N_v) ≥ 0 and sqrt(N_c N_v) = sqrt(N_c) sqrt(N_v). If either quantity is zero, the result is zero. The shorthand sqrtNcNv may appear in notes or code, but the mathematically precise form is sqrt(N_c N_v).

Computation can be done directly by multiplying the two quantities and taking the square root, or by taking the square roots separately and multiplying: sqrt(N_c N_v) = sqrt(N_c) sqrt(N_v). For example, with N_c = 9 and N_v = 16, sqrt(N_c N_v) = sqrt(144) = 12.

Applications of this quantity occur when combining two counts or measurements in a symmetric, scale-free way. It can serve as a normalization factor or a component in indices and similarity measures involving co-occurrence or joint counts. Because it is a geometric mean, it tends to dampen the influence of very large disparities between N_c and N_v compared with the arithmetic mean.

See also: Geometric mean; Square root; Normalization.