# 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.

## characteristic equation

/karɪktəˌrɪstɪk ɪˈkweɪʒn/