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Vector Space Math Operations

A number of math operations are available in the vector_space class. These include addition, subtraction and intersection. The meanings of these operations are described in detail below. For all these operations, either a new vector space can be created (i.e. X = V + W) or the result can be stored into one of the operands (i.e. X += V).

Given two spaces V and W, then X = V + W is the vector space made up of all possible combinations x = v + w, where v is an element of V and w is an element of W. Both V and W must have the same space dimension. For example:

{(1, 0)} + {(1, 1)} = {(1, 0), (0, 1)}

Given two spaces V and W, then X = V - W is the vector space V with all the common directions removed. Both V and W must have the same space dimension.

For example:

{(1, 0), (0, 1)} - {(1, 1)} = {(1, -1)}

The multiplication operator is used for vector space intersection. Given two spaces V and W, then X = V * W is the space whose vectors are in both V and W. Both V and W must have the same space dimension. For example:

{(1, 0)} * {(0, 1)} = {}

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