A vector space is a mathematical structure formed by a collection of vectors, which can be added together and multiplied by scalars. Vectors can represent quantities with both magnitude and direction, such as forces or velocities. The operations of addition and scalar multiplication must satisfy certain properties, like associativity and distributivity, to ensure the structure behaves consistently. In a vector space, the vectors can be represented in various forms, such as 2D or 3D coordinates. Common examples include Euclidean spaces and function spaces. Vector spaces are fundamental in many areas of mathematics and physics, providing a framework for solving linear equations and modeling various phenomena.