vector space

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vector space (plural vector spaces)

1. (algebra, geometry, topology) A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.

   A vector space is a set of vectors which can be linearly combined.

   Each vector space has a basis and dimension.

• linear space

• module
• free module

• algebra over a field
• Banach space
• Euclidean space
• inner product space
• normed vector space
• quadratic space
• real vector space

• linear subspace
• subspace
• vector