Home / All Definitions / Numbers & Symbols / Pre-Calculus / Rho (Ρ, ρ) Definition

Rho (Ρ, 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 Phoenician letter res. Its uppercase form uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings.

The characters ρ and Ρ are also conventionally used outside the Greek alphabetical context in science and mathematics:

In the physical sciences to represent:

Densities: mass density, air density or charge density (ρ).

Resistivity (ρ).

Rho meson (ρ

^{+}, ρ^{−}, ρ^{0}).General quantum states.

Hammett Equation, ρ is used to represent the reaction constant, this is independent of the position and nature of the substituents of the benzene ring.

In mathematics to represent:

A length coordinate in polar, cylindrical, spherical, and toroidal coordinate systems, and toroidal and poloidal coordinates of the Earth's magnetic field.

The correlation coefficient of a population parameter.

The spectral radius of a matrix A denoted as ρ(A).

The plastic number.

The prime constant.

The sensitivity to interest rates of a pricing function.

The expected return of a given policy (π) in reinforcement learning, denoted ρ

^{π}In economics to represent the discount rate of future cash flows.

In molecular biology to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as ϱ, to avoid confusion with the Latin letter p.

In molecular biology to represent the Rho family of GTPases, important for cytoskeletal dynamic regulation.

In ecology to represent the population damping ratio where ρ = λ1 / |λ2|.

In computer programming:

The lower-case rho ρ means reshape in the APL programming language, and by extension also queries shape.

The lower-case rho ρ is used for the unary rename operation in relational algebra.

In statistics to represent Spearman's rank correlation coefficient, commonly known as Spearman's rho.

In options theory to represent the rate of change of a portfolio with respect to interest rates.

The letters of the Ancient Greek Alphabet, which are frequently utilized in math and science:

“Rho.” Wikipedia, Wikimedia Foundation, 30 Apr. 2020, en.wikipedia.org/wiki/Rho.

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