Vector-space meaning

A system consisting of a set of generalized vectors and a field of scalars, having the same rules for vector addition and scalar multiplication as physical vectors and scalars.
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A set of generalized vectors and a field of scalars, together with rules for their addition and multiplication (the same rules used for ordinary vectors and scalars).
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(mathematics) A type of set of vectors that satisfies a specific group of constraints.

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

Each vector space has a basis and dimension.

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