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# Finding eigenvalues and eigenvectors with NumPy

Eigenvalues are scalar solutions to the equation `Ax = ax`, where `A` is a two-dimensional matrix and `x` is a one-dimensional vector. Eigenvectors are vectors corresponding to eigenvalues.

### Note

Eigenvalues and eigenvectors are fundamental in mathematics and are used in many important algorithms, such as Principal Component Analysis (PCA). PCA can be used to simplify the analysis of large datasets.

The `eigvals()` subroutine in the `numpy.linalg` package computes eigenvalues. The `eig()` function gives back a tuple holding eigenvalues and eigenvectors.

We will obtain the eigenvalues and eigenvectors of a matrix with the `eigvals()` and `eig()` functions of the `numpy.linalg` subpackage. We will check the outcome by ...

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