TeXipedia

Eta

Represents the uppercase Greek letter used in mathematics, physics, and engineering for various quantities and coefficients.

Overview

Commonly employed across scientific and mathematical contexts to denote specific concepts or variables:

  • Frequently used in physics to represent efficiency or performance coefficients
  • Appears in fluid dynamics equations and thermodynamic calculations
  • Serves as a standard variable in statistical analysis and probability theory
  • Often represents viscosity-related parameters in mechanical engineering

The uppercase variant is less common than its lowercase counterpart but maintains specific technical meanings in certain fields.

Examples

Using the capital Eta symbol in a statistical hypothesis.

H0:H=0H_0: \Eta = 0 
H_0: \Eta = 0

Representing an efficiency coefficient in thermodynamics.

H=WoutQin\Eta = \frac{W_{out}}{Q_{in}} 
\Eta = \frac{W_{out}}{Q_{in}}

Denoting a matrix of correlation coefficients.

H=(1η12η211)\mathbf{\Eta} = \begin{pmatrix} 1 & \eta_{12} \\ \eta_{21} & 1 \end{pmatrix} 
\mathbf{\Eta} = \begin{pmatrix} 1 & \eta_{12} \\ \eta_{21} & 1 \end{pmatrix}