Eigenvalues and Eigenvectors

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The vector $\bf v$ is an eigenvector of $A$ with eigenvalue $\lambda$ if ${\bf v} \ne {\bf 0}$ , and $A*{\bf v} = \lambda {\bf v}$ meaning multiplying $\bf v$ on the left by the matrix $A$ has the same effect as multiplying it by the scalar $\lambda$ .

Given a numerical matrix $A$ , our goal will be to determine the eigenvalues and eigenvectors of $A$ .