Rho (uppercase Ρ, lowercase ρ or ϱ) is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Semitic Rêš "head" (see Resh). Its uppercase form is not to be confused with the Roman letter P. Rho is generally classed as a liquid (together with lambda and sometimes the nasals mu and nu), which has important implications for morphology. It is pronounced similarly to the letter r in languages with a Latin-derived alphabet. In polytonic orthography a rho at the beginning of a word is conventionally written with a rough breathing (equivalent to h) — ῥ — and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second — ῤῥ — apparently reflecting an aspirated or voiceless pronunciation in Ancient Greek, hence the various Greek-derived English words which start with rh or contain rrh. The name of the letter is written in Greek as ῥῶ (polytonic) or ρώ (monotonic). Letters that arose from rho include Roman R and Cyrillic Er (Р).
Common notational uses
- lower-case rho ρ
The lower-case rho ρ has a special meaning in the APL programming language. It is commonly used in physics to represent density (lower-case) and resistivity (lower-case), in mathematics to represent the radius in a system of spherical polar coordinates, in economics to represent the discount rate of future pence cash flows and in molecular biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as ϱ ("rho symbol" U+03F1), to avoid confusion with the Latin letter p. In matrix analysis, it is used to represent the Spectral radius of a matrix <math>A</math> denoted as <math>\rho(A)</math>. In LaTeX, the symbols are \Rho (<math>\Rho</math>), \rho (<math>\rho</math>), and \varrho (<math>\varrho</math>). It is used in statistics to represent the correlation coefficient of a population parameter.
