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

From Textbooks • Mar. 30, 2016

The characteristic equation is very important in finding solutions to differential equations of this form.

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

Things are a little more complicated if the characteristic equation has a repeated real root, λ.

From Textbooks • Mar. 30, 2016

M. Van der Waals has sought out the modifications which must be introduced into the simple characteristic equation to bring it nearer to reality.

From The New Physics and Its Evolution by Poincaré, Lucien