When Are Two Subspaces Complementary?

Two subspaces of a vector space are said to be complementary if their direct sum gives the entire vector space as a result.

How do you prove two subspaces are complementary?

Also, from my lecture notes it mentions a certain proposition that when applied to this question, I can say that subspaces K and L of a vector space U are complementary if and only if each vector u∈U can be written uniquely as u=k+l, where k∈K and l∈L.

What do you mean by complementary subspace?

In linear algebra, a complement to a subspace of a vector space is another subspace which forms a direct sum. Two such spaces are mutually complementary. ... The complementarity relation is symmetric, that is, if W is a complement of U then U is also a complement of W.