One of the mysteries of the English language finally explained.

# Definition of *characteristic equation* in US English:

## characteristic equation

### noun

1Mathematics. More fully "Gaussor Gauss's characteristic equation". An equation expressing the curvature of a surface in terms of certain parameters of the surface.

2Mathematics. A quadratic equation in which the derivatives in a second order differential equation are replaced by scalar variables, obtained to facilitate the solution of the differential equation.

3Mathematics. Any equation that in some way characterizes or summarizes something.

4Physics. An equation relating the temperature, pressure, and volume of a gas; specifically the equation PV = RT.

5Mathematics. An equation in which the characteristic polynomial of a particular matrix is equated to zero, which when solved gives the eigenvalues (latent roots) of the matrix.

**Origin**

Early 19th century; earliest use found in Philosophical Magazine. From characteristic + equation.