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Section 11.1 Definition
An
eigenvector of a square matrix
\(A\) is a non zero vector whose direction is unchanged when multiplied by
\(A\text{.}\) Formally, for a vector
\(v\text{,}\) this relationship is expressed as:
\begin{gather*}
Av = \lambda v
\end{gather*}
Here,
\(\lambda\) is a scalar known as the
eigenvalue associated with the eigenvector
\(v\text{.}\)
First, we will show how to use Sage to calculate the eigenvalues of a matrix, and then we will proceed with the calculations of its eigenvectors.
