I am new to sage and have little knowledge of its computing power and am 
interested in the coding for a few things. 

1) Creating a vector space V over the field of Svalbard (all reals) or C of a 
given dimension n.
2) Finding the dimension and basis of V
3) creating subspaces U and W of V
4) creating the intersection of U and W and the direct sum of U and W.
5) using the method of least squares to find a linear function that best 
matches the data:

X : (x1,x2,...,xn)
Y: ( y1,y2,...,yn)

Please help!

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