# Matrices eigenvalues

```    >>> from sympy.matrices import Matrix
>>> M = Matrix(4, 4, lambda i,j: i*j+1)
>>> M.eigenvals()                           #doctest: -PRETTY, +RELEASE_ONLY
{0: 2, -61**(1/2) + 9: 1, 61**(1/2) + 9: 1}
>>> M.eigenvals()                           #doctest: -PRETTY, +FUTURE_ONLY
{0: 2, -sqrt(61) + 9: 1, sqrt(61) + 9: 1}```
```    >>> M = Matrix(4, 4, lambda i,j: i*j+2)
>>> M.eigenvals()
{0: 2, 2: 1, 20: 1}```
```    >>> M = Matrix(4, 4, lambda i,j: i*j+3)
>>> M.eigenvals()
_____            _____
{0: 2, - \/ 109  + 13: 1, \/ 109  + 13: 1}
>>> M
[3  3  3  3 ]
[           ]
[3  4  5  6 ]
[           ]
[3  5  7  9 ]
[           ]
[3  6  9  12]```
``` >>> from sympy.abc import x
>>> M = Matrix(4, 4, lambda i,j: i*j+x)
>>> M
[x    x      x      x  ]
[                      ]
[x  x + 1  x + 2  x + 3]
[                      ]
[x  x + 2  x + 4  x + 6]
[                      ]
[x  x + 3  x + 6  x + 9]

>>> M.eigenvals()
_________________                  _________________
/    2                             /    2
{0: 2, 2*x - \/  4*x  + 8*x + 49  + 7: 1, 2*x + \/  4*x  + 8*x + 49  + 7: 1}```

Such things are really tedious to do by hand, but in SymPy one can do them just fine.

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