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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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