# characteristic equation

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

- Physics. equation of state.

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## Origin of characteristic equation^{}

First recorded in 1920–25

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018