In linear algebra, the characteristic equation of a square matrix A is the equation in one variable λ

det(A - λI) = 0

where I is the identity matrix. The solutions of the characteristic equation are precisely the eigenvalues of the matrix A. The polynomial to the left of "=" is the characteristic polynomial of the matrix.

For example, for the matrix

the characteristic equation is

The eigenvalues of this matrix are therefore 20 and 25.