Characteristic polynomial

The characteristic polynomial of a square matrix is a polynomial that is invariant under matrix similarity and has the eigenvalues of the matrix as eigenvectors. It is defined as P(x) = det(xI – A), where x is the variable of the polynomial and I is the corresponding identity matrix.


Given a matrix, it returns its characteristic polynomial in the variable x 1.

characteristic_polynomial(Matrix, Expression)

Given a matrix and an expression, it returns its characteristic polynomial evaluated in the desired expression.

Below is a complete list of options that may be used in the characteristic_polynomial function.

Option Description Format Default value
method We can choose the method to be used from the following: adjoint_matrix, determinant, hessenberg and hessenberg_householder. {method=”adjoint_matrix”} hessenberg_householder
exact_computations We can choose to perform or not exact computations. {exact_computations=false} true, but depends on the input