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Eta (Η, η) Definition

Eta (Η, η) is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its sound value in the classical Attic dialect of Ancient Greek was a long vowel [ɛː], raised to [i] in hellenistic Greek, a process known as iotacism. In the ancient Attic number system (Harodianic or acrophonic numbers), the number 100 was represented by Η, because it was the initial of ΗΕΚΑΤΟΝ, the ancient spelling of ἑκατόν = one hundred. In the latter system of (Classical) Greek numerals it has a value of 8. Eta was derived from the Phoenician letter heth. Letters that arose from eta include the Latin H and the Cyrillic letter И.

Usage in Mathematics & Science

The uppercase Eta (Η) is used for:

  • The uppercase letter Η is used as a symbol in textual criticism for the Alexandrian text-type (from Hesychius, its once-supposed editor).

  • In chemistry, the letter Η as symbol of enthalpy sometimes is said to be a Greek eta, but since enthalpy comes from ἐνθάλπος, which begins in a smooth breathing and epsilon, it is more likely a Latin Η for 'heat'.

  • In information theory the uppercase Greek letter Η is used to represent the concept of entropy of a discrete random variable.

The lowercase Eta (η) is used for:

  • Thermodynamics, the efficiency of a Carnot heat engine, or packing fraction.

  • Chemistry, the hapticity, or the number of atoms of a ligand attached to one coordination site of the metal in a coordination compound. For example, an allyl group can coordinate to palladium in the η1 mode (only one atom of an allyl group attached to palladium) or the η3 mode (3 atoms attached to palladium).

  • Optics, the electromagnetic impedance of a medium, or the quantum efficiency of detectors.

  • Particle physics, to represent the η mesons.

  • Experimental particle physics, η stands for pseudorapidity.

  • Cosmology, η represents conformal time; dt = adη.

  • Cosmology, baryon–photon ratio.

  • Relativity and Quantum field theory (physics), η (with two subscripts) represents the metric tensor of Minkowski space (flat spacetime).

  • Statistics, η2 is the "partial regression coefficient". η is the symbol for the linear predictor of a generalized linear model, and can also be used to denote the median of a population, or thresholding parameter in Sparse Partial Least Squares regression.

  • Economics, η is the elasticity.

  • Astronomy, the seventh-brightest (usually) star in a constellation. See Bayer designation.

  • Mathematics, η-conversion, see lambda calculus.

  • Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass eta function.

  • In category theory, the unit of an adjunction or monad is usually denoted η.

  • Biology, a DNA polymerase found in higher eukaryotes and implicated in Translesion Synthesis.

  • Neural network backpropagation, and stochastic gradient descent more generally, η stands for the learning rate.

  • Telecommunications, η stands for efficiency.

  • Electronics, η stands for the ideality factor of a bipolar transistor, and has a value close to 1.000. It appears in contexts where the transistor is used as a temperature sensing device, e.g. the thermal "diode" transistor that is embedded within a computer's microprocessor.

  • Power electronics, η stands for the efficiency of a power supply, defined as the output power divided by the input power.

  • Atmospheric science, η represents absolute atmospheric vorticity.

  • Rheology, η represents viscosity.

  • Oceanography, η is the measurement (usually in meters) of sea-level height above or below the mean sea-level at that same location.

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

“Eta.” Wikipedia, Wikimedia Foundation, 6 Apr. 2020, en.wikipedia.org/wiki/Eta.

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