The "Direct Sum" is a concept in mathematics, particularly in linear algebra and abstract algebra. It refers to a way of combining two or more vector spaces or modules into a new one. When two spaces are combined using the direct sum, every element in the resulting space can be uniquely expressed as a sum of elements from each of the original spaces. This property makes direct sums useful for simplifying complex structures. In notation, if V and W are two vector spaces, their direct sum is denoted as V ⊕ W. This means that any vector in V ⊕ W can be written as v + w, where v is from V and w is from W. The direct sum is particularly important in areas like representation theory and functional analysis, where it helps in understanding the structure of spaces.