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# characteristic equation

[ kar-ik-t*uh*-**ris**-tik i-**kwey**-zh*uh*n, -sh*uh*n ]

## noun

*Mathematics.*- the characteristic polynomial of a given matrix, equated to zero.
- Also called
**aux·il·ia·ry e·qua·tion**[awg-, zil, -y, uh, -ree i-, kwey, -zh, uh, n, -sh, uh, n, -, zil, uh, -]. 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.

*Physics.*equation of state.

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## Word History and Origins

Origin of characteristic equation^{1}

First recorded in 1920–25

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## Example Sentences

In the next place apply the surface characteristic equation to any point on a charged conductor at which the surface density is σ.

From Project Gutenberg

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