Meaning of characteristic equation

characteris'tic equa'tion

Pronunciation: [key]
    1. the characteristic polynomial of a given matrix, equated to zero.
    2. Also calledauxiliary 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.
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Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.