direct sum

C1Linear Algebra

(technical, academic)A subspace formed by the set of all possible sums of elements from two subspaces, where each element can be uniquely represented, and their intersection is only the zero vector.

Example

• In \\mathbb{R}^2, the direct sum of the x-axis and y-axis forms the entire plane.

C2Abstract Algebra

(technical, academic)A group formed by ordered tuples, where each tuple element belongs to one of the groups, and addition is performed component-wise.

Example

• The direct sum of two cyclic groups of order 2 is a group of order 4.

C2Topology

(technical, academic)A topological space formed by taking the disjoint union of several spaces and equipping it with a topology that makes the inclusion maps continuous.