characteristic equation

American  

[kar-ik-tuh-ris-tik i-kwey-zhuhn, -shuhn] / ˌkær ɪk təˈrɪs tɪk ɪˈkweɪ ʒən, -ʃən /

noun

1. Mathematics.

   1. the characteristic polynomial of a given matrix, equated to zero.

   2. Also called auxiliary equation.  an equation with one variable and equated to zero, which is derived from a given linear differential equation and in which the coefficient and power of the variable in each term correspond to the coefficient and order of a derivative in the original equation.

2. Physics. equation of state.

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Etymology

Origin of characteristic equation

First recorded in 1920–25

Example Sentences

The form of the general solution varies, depending on whether the characteristic equation has distinct, real roots; a single, repeated real root; or complex conjugate roots.

From Textbooks • Mar. 30, 2016

By the quadratic formula, the roots of the characteristic equation are 1 ± 2i.

From Textbooks • Mar. 30, 2016

For example, the differential equation y″ + 12y′ + 36y = 0 has the associated characteristic equation λ2 + 12λ + 36 = 0.

From Textbooks • Mar. 30, 2016

We call this the characteristic equation of the differential equation.

From Textbooks • Mar. 30, 2016

In reality, this is simply due to the fact that the characteristic equation only contains three constants.

From The New Physics and Its Evolution by Poincaré, Lucien