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

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

From Textbooks • Mar. 30, 2016

We call this the characteristic equation of the differential equation.

From Textbooks • Mar. 30, 2016

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

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

From Textbooks • Mar. 30, 2016

Given the specific heat as a function of the temperature, its variation with pressure may be determined from the characteristic equation of the gas.

From Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 1 "Calhoun" to "Camoens" by Various