Direct sum of vector spaces ↩

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created: 2021-12-10 18:52:59
modified: 2022-01-16 13:48:19

, we will construct a new vector space

called the direct sum of

and

. The set of vectors in

is just the set of all ordered pairs

with

and

¹. We add these pairs this way:

And for a scalar we define:

The set forms a vector space this way since and do as well.

Zero vector

The zero vector in is .

As we can see in Basis of direct sum vector space, the dimension of is: