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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

Related Definitions

Sources

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

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