Vectors as matrices

There are very good reasons that vectors should be treated as 1 x n and $n\times1$ matrices:

• This is so when n x m matrices are considered as linear transforms from m-dimensional to n-dimensional spaces.
• Vectors can be sliced off matrices. Matrices can be built from vectors. They obey the same rules. Most operations should be valid for both.
• All the rules for vectors and covectors map naturally into the rules for column and row vectors.

The array type in NumPy behaves more like a diagonal matrix than ordinary vectors. Therefore we implement vectors as matrices instead.

However, it might be worthwhile to implement a Vector subclass for efficiency reasons. I do not know how to let Matrix(a) sometimes return a Vector depending on a.shape.