Rho

How to read it

Dictionary.com and the Collins English Dictionary give the pronunciation “roh” (/roʊ/, /rəʊ/); Collins describes rho as a consonant transliterated as r or rh. The capital Ρ has the shape of the Latin P, and Dictionary.com prints it with a Latin P, but it stands for the r sound and a separate character (Latin P is U+0050).

Also searched as: rho letter, rho symbol, ρ, Ρ, ρ meaning.

Capital and small forms

Unicode describes ϱ as a technical symbol.

Rho in science and statistics

Density is ρ = m / V, mass divided by volume, in kilograms per cubic metre (NIST’s Guide for the Use of the SI; OpenStax). NIST notes that ρ is also used for charge density, ρ = Q / V. In statistics ρ is the population correlation coefficient; OpenStax’s Introductory Statistics writes the sample correlation coefficient, calculated from data, as r.

In AI and machine learning

In PyTorch’s Adadelta optimiser, rho (ρ) is the coefficient used for computing a running average of squared gradients, 0.9 by default.

In quantum physics

ρ is the density matrix, also called the state operator. MIT’s 22.51 notes describe the state operator for a pure state |ψ⟩ as the outer product ρ = |ψ⟩⟨ψ|, written in Bra-ket notation (|ψ⟩); MIT’s 8.06 notes give the same density matrix.