Function Repository Resource:

# IntersectionBasis

Find a basis for the intersection of subspaces of ℝ^n

Contributed by: Dennis M Schneider
 ResourceFunction["IntersectionBasis"][list1,list2,…] finds a basis for the intersection of the subspaces of spanned by list1,list2, ….

## Details and Options

The method is based on expressing each subspace as the null space of a matrix and then finding the null space of the matrix obtained by stacking these matrices vertically.
The empty list spans the trivial subspace.

## Examples

### Basic Examples (4)

The intersection of two three-dimensional subspaces of :

 In[1]:=
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Two subspaces are called disjoint if their intersection is the trivial space, and a basis for the trivial subspace is the empty list. These two subspaces are disjoint:

 In[2]:=
 Out[2]=

All vectors in the lists must have the same size:

 In[3]:=
 Out[3]=

Again, the vectors in the list must have the same size; the sizes of the vectors in the second list are 4 and 0:

 In[4]:=
 Out[4]=

Compare with the following. The first list has two elements, the second has one, and the third also has one:

 In[5]:=
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## Publisher

Dennis M Schneider

## Version History

• 1.0.0 – 24 September 2019