## Time for action – determining eigenvalues and eigenvectors

Let's calculate the eigenvalues of a matrix:

1. Create a matrix as shown in the following:

```A = np.mat("3 -2;1 0")
print("A\n", A)```

The matrix we created looks like the following:

```A
[[ 3 -2]
[ 1  0]]
```
2. Call the `eigvals()` function:

`print("Eigenvalues", np.linalg.eigvals(A))`

The eigenvalues of the matrix are as follows:

```Eigenvalues [ 2.  1.]
```
3. Determine eigenvalues and eigenvectors with the `eig()` function. This function returns a tuple, where the first element contains eigenvalues and the second element contains corresponding eigenvectors, arranged column-wise:

```eigenvalues, eigenvectors = np.linalg.eig(A)
print("First tuple of eig", eigenvalues)
print("Second tuple of eig\n", eigenvectors)```

The eigenvalues and eigenvectors appear as follows:

```First tuple of eig [ 2.  1.]
Second tuple of eig
[[ 0.89442719  0.70710678]
[ 0.4472136   0.70710678]]
```
4. Check the result with the `dot()` function by calculating the right and left side of the eigenvalues equation...