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Function Repository Resource:

SumBasis

Source Notebook

Find a basis for the sum of a list of subspaces of ℝ^n

Contributed by: Dennis M Schneider

ResourceFunction["SumBasis"][list1,list2,]

returns a basis for the sum of the subspaces of n spanned by list1,list2,….

Examples

Basic Examples

The sum of a two-dimensional subspace and a three-dimensional subspace of 4:

In[1]:=
ResourceFunction[
 "SumBasis"][{{1, 1, 1, 1}, {2, 2, 3, 4}}, {{2, 3, 4, 7}, {1, 0, 1, 0}, {0, 1, 0, 3}}]
Out[1]=

The sum of a subspace and a subspace of the subspace:

In[2]:=
ResourceFunction[
 "SumBasis"][{{1, 1, 1, 1}, {2, 2, 3, 4}}, {{3, 3, 5, 7}}]
Out[2]=

A sum of three subspaces:

In[3]:=
ResourceFunction[
 "SumBasis"][{{1, 1, 1, 1, 1}, {1, 2, 3, 4, 5}}, {{1, 0, 1, 0, 1}, {0,
    1, 0, 3, 1}}, {{1, 1, 1, 3, 2}, {2, 3, 4, 5, 6}}]
Out[3]=

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