# Eigenvalues and Eigenvectors

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#### find the eigenvalues eigenvectors of : input

$$A=\left[ \begin{array}{ccc} -11 & 11 & -8 \\\\ 2 & 8 & -2 \\\\ 3 & -6 & 13 \end{array} \right]$$

#### Solution

The eigenvalues are: $$14.319845825042$$ $$-11.093328801961$$ $$6.7734829769186$$ The eigenvector are: $$A=\left[ \begin{array}{ccc} 0.42789507478398 & 0.98126963760267 & 0.1773255664043 \\\\ 0.392988982286 & -0.11868109115281 & 0.74997514516667 \\\\ -0.81391981470992 & -0.15173891037536 & 0.63725420762175 \end{array} \right]$$

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What are Eigenvalues and Eigenvectors?

In mathematic an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by, is the factor by which the eigenvector is scaled.

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