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.
Syntax
characteristic_polynomial(Matrix)
characteristic_polynomial(Matrix, Expression)
Description
Given a matrix, it returns its characteristic polynomial in the variable .
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Given a matrix and an expression, it returns its characteristic polynomial evaluated in the desired expression.
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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: | | |
exact_computations | We can choose to perform or not exact computations. | | |