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# 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.

## Usage in Mathematics & Science

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, ρ0).

• 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 ρπ

• 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.

## Greek Alphabet

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

 Greek Alphabet Symbol Letter Symbol Letter Uppercase Lowercase Uppercase Lowercase Α α Alpha Ν ν Nu Β β Beta Ξ ξ Xi Γ γ Gamma Ο ο Omicron Δ δ Delta Π π Pi Ε ε Epsilon Ρ ρ Rho Ζ ζ Zeta Σ σ Sigma Η η Eta Τ τ Tau Θ θ Theta Υ υ Upsilon Ι ι Iota Φ φ Phi Κ κ Kappa Χ χ Chi Λ λ Lambda Ψ ψ Psi Μ μ Mu Ω ω Omega

### Sources

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

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