# Linear Algebra Refresher

## Grundgerüst

```python
# -*- coding: iso-8859-15 -*
from math import sqrt

class Vector(object):
   def __init__(self, coordinates):
      try:
         if not coordinates:
            raise ValueError
         self.coordinates = tuple(coordinates)
         self.dimension = len(coordinates)
         
      except ValueError:
         raise ValueError('Die Koordinaten dürfen nicht leer sein')
         
      except TypeError:
         raise TypeError('Die Koordinaten müssen iterierbar sein')
                
   def __str__(self):
      return 'Vector: {}'.format(self.coordinates)
  
   def __eq__(self, v):
      return self.coordinates == v.coordinates
```

## Addition von Vektoren

$\left[ {\begin{array}{*{20}{c}}
5\\
0
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
2\\
2
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
7\\
2
\end{array}} \right]$

```python
veka1 = Vector([0,5])
veka2 = Vector([2,2])

print (veka1.plus(veka2))
```

<img src="vektor_add.png" style="zoom:40%;" />

```python
veka1 = Vector([0,5])
```

$\left[ {\begin{array}{*{20}{c}}
7\\
2
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
-3\\
2
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
4\\
4
\end{array}} \right]$

<img src="vector_add_2.png" style="zoom:30%;" />