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The characteristic polynomial of a matrix.

Let A be a square matrix of order n. The determinant $P_{A}(\lambda)=\vert A- \lambda I\vert$ is a polynomial of degree n in the variable $\lambda$. It is called the characteristic polynomial of the matrix A.

Example 11.1.1       

If $A= \begin{pmatrix}1 & 2 & 1 \\ 0 & 1 & 3 \\ 1 & 0 & -2 \end{pmatrix}$, then

\begin{displaymath}P_A(\lambda)= \begin{vmatrix}1- \lambda & 2 & 1 \\ 0 & 1-\lam...
...3 \\ 1 & 0 & -2-\lambda \end{vmatrix}=-\lambda^3 +4 \lambda +3
\end{displaymath}



Noah Dana-Picard
2001-02-26