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

We call this the characteristic equation of the differential equation.

From Textbooks • Mar. 30, 2016

For example, the differential equation y″ − 2y′ + 5y = 0 has the associated characteristic equation λ2 − 2λ + 5 = 0.

From Textbooks • Mar. 30, 2016

For example, the differential equation y″ + 9y′ + 14y = 0 has the associated characteristic equation λ2 + 9λ + 14 = 0.

From Textbooks • Mar. 30, 2016

From the ascertained behaviour in certain respects of gaseous media we are able to construct their characteristic equation, and correlate their remaining relations by means of its consequences.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 3 "Electrostatics" to "Engis" by Various