characteristic equation

[ kar-ik-tuh-ris-tik i-kwey-zhuhn, -shuhn ]

noun

1. Mathematics.
   1. the characteristic polynomial of a given matrix, equated to zero.
   2. 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.
2. Physics. equation of state.

Word History and Origins

Origin of characteristic equation¹

First recorded in 1920–25

Example Sentences

We can, however, obtain another equation called the “surface characteristic equation” as follows:—Suppose a very small area dS described on a conductor having a surface density of electrification σ.

From Project Gutenberg

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

Now each phase has its own characteristic equation, giving a relation between δp, δT, and δμ1, ... δμn, or such of the latter as are independent; if r phases coexist, there are r such relations; hence the number of possible independent variations, including those of v and T, is reduced to m − r + 2, where m is the number of independently variable chemical constituents which the system contains.

From Project Gutenberg

Interfacial Phenomena: Liquid Films.—The characteristic equation hitherto developed refers to the state of an element of mass in the interior of a homogeneous substance: it does not apply to matter in the neighbourhood of the transition between two adjacent phases.

From Project Gutenberg

From the ascertained behaviour in certain respects of gaseous media we are able to construct their characteristic equation, and correlate their remaining relations by means of its consequences.

From Project Gutenberg