FANDOM


The characteristic polynomial of a matrix A is the polynomial satisfies the equation

|\lambda I_n - A| = 0

The roots of this function will be the eigenvalues of the matrix.

Example

Given the matrix

A = \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix}

The characteristic polynomial will be

\begin{vmatrix} \lambda I - \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix} \end{vmatrix} = \begin{vmatrix} \lambda \begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix} - \begin{bmatrix}3 & 0 \\-1 & -1 \end{bmatrix} \end{vmatrix} = 0
\begin{vmatrix} \lambda - 3 & 0 \\1 & \lambda + 1 \end{vmatrix} = (\lambda - 3) (\lambda + 1) - (0)(1) = (\lambda - 3) (\lambda + 1) = 0

The eigenvalues of A will be -1 and 3.

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.