characteristic equation

This term is a specialized technical expression used almost exclusively within linear algebra and differential equations. It describes the specific polynomial equation used to determine the eigenvalues of a square matrix, serving as the bridge between a matrix's structural properties and its scalar characteristics.

In a pedagogical context, it is often introduced as the determinant of the matrix subtracted by a scalar multiple of the identity matrix. Because it is a compound noun referring to a specific mathematical object, it is treated as a countable entity in academic discourse, though it is rarely used in the plural unless discussing multiple different matrices.