What is it
A vector space is a set of objects (not necessarily arrows or lists of numbers) that can be added together and scaled by numbers while obeying a consistent set of algebraic rules — covering basis, dimension, and subspaces.
Why it matters
Vector spaces are one of the great unifying abstractions in mathematics — the same theory applies equally to arrows in 3D space, polynomials, functions, and matrices, once you recognise they all satisfy the same underlying rules.
Exam tip
To prove a set is a subspace, check the three conditions in order: it contains the zero vector, it's closed under addition, and it's closed under scalar multiplication — skipping the zero-vector check is a common way to miss an easy first step.
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