Abstract Linear Algebra II
Closure under addition refers to the property that when you take any two elements from a set and add them together, the result is also an element of that same set. This idea is crucial for defining vector spaces and subspaces, as it ensures that the set remains intact when performing the operation of addition, which is one of the foundational operations in linear algebra. When a set possesses this property, it helps to confirm whether the set can be classified as a vector space or a subspace, and is also significant in understanding how different subspaces can combine through sum and direct sum operations.
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