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Let U1 and U2 be two subspaces of the same vector space V. The sum of these subspaces, denoted U1 + U2, is the set of all the sums
the sum is a direct sum and is denoted
then U1 and U2 are supplementary subspaces.
be the vector space of all the functions defined on
the subspace of all the odd (resp. even) functions from
to itself. Then
Direct sum of a plane and a line.
be a finite-dimensional space and let V1
be two subspaces such that
This is linked to Thm 4.5.