Basis of direct sum vector space ↩

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created: 2021-12-10 19:04:49
modified: 2022-01-10 04:13:04

and are vector spaces, is their direct sum.
Statement: If is a basis for and is a basis for , then

is a basis for .

Proof

Given we have:

Then , also uniquely. QED

Corollary

The dimension of the resulting space: