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Characteristic polynomial
Reading time: 1minThe 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.
Syntax
characteristic_polynomial(Matrix)
characteristic_polynomial(Matrix, Expression)
Description
Given a matrix, it returns its characteristic polynomial in the variable x1.
Given a matrix and an expression, it returns its characteristic polynomial evaluated in the desired expression.
Options
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 |