- #1
kamil
- 6
- 0
I find it rather tedious to calculate the eigenvalues of a 3x3 matrix. For example
[tex]The \emph{characteristic polynomial} $\chi(\lambda)$ of the
3$3 \times 3$~matrix
\[ \left( \begin{array}{ccc}
1 & -1 & -1 \\
-1 & 1 & -1 \\
-1 & -1 & 1 \end{array} \right)\]
is given by the formula
\[ \chi(\lambda) = \left| \begin{array}{ccc}
1-\lambda & -1 & -1 \\
-1 & 1-\lambda & -1 \\
-1 & -1 & 1-\lambda \end{array} \right|.\] [/tex]
Now if I do this by develloping the minors I get a cubic equation and I can't solve it without at least 30 minutes. I find it time consuming, especially during an exam.
[tex]The \emph{characteristic polynomial} $\chi(\lambda)$ of the
3$3 \times 3$~matrix
\[ \left( \begin{array}{ccc}
1 & -1 & -1 \\
-1 & 1 & -1 \\
-1 & -1 & 1 \end{array} \right)\]
is given by the formula
\[ \chi(\lambda) = \left| \begin{array}{ccc}
1-\lambda & -1 & -1 \\
-1 & 1-\lambda & -1 \\
-1 & -1 & 1-\lambda \end{array} \right|.\] [/tex]
Now if I do this by develloping the minors I get a cubic equation and I can't solve it without at least 30 minutes. I find it time consuming, especially during an exam.