direct sum

If, in addition, this is a direct sum, we write .

For a direct sum this is clear, as one can inject from or project to the summands.

This means that we can form finite direct sums and direct products.

The finiteness condition is built into the definition of the direct sum.

This ordering is more natural if one thinks of the real space as a direct sum, as discussed below.

The right hand side is a direct sum of fields.

The wedge product endows the direct sum of these groups with a ring structure.

The direct sum of the complex field with itself is denoted .

The direct sum with this norm is again a Banach space.

Decomposition of a vector space into direct sums is not unique in general.