Vector space

A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra.

Related Topics:
Mathematics - Linear algebra

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If one considers geometrical vectors, and the operations one can perform upon these vectors such as addition of vectors, scalar multiplication, with some natural constraints such as closure of these operations, associativity of these and combinations of these operations, and so on, we arrive at a description of a mathematical structure which we call a vector space.

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The "vectors" need not be geometric vectors in the normal sense, but can be any mathematical object that satisfies the following vector space axioms. Polynomials of degree ≤n with real-valued coefficients form a vector space, for example. It is this abstract quality that makes it useful in many areas of modern mathematics.

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