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Vector space

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      1 min de lecture

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      llms.txt

    Not to be confused with vector field, but a vector space is a set whose vectors can be scaled by any given scalars

    A vector space have all basic properties of a set, including associative, commutative, identity, inverse, distributivity

    coordinates, and subspace

    We can then take a look for a set of GG of a FF-vector space VV, the following properties:

    linear combination

    a1g1+a2g2+⋯+angna_{1} \mathbf{g}_1 + a_{2} \mathbf{g}_2 + \cdots + a_{n} \mathbf{g}_n

    where scalars a1,…ana_1, \ldots a_{n} is the coefficient of the linear combination

    linear independent, span, basis, subspace

    See also linearly dependent, span and basis

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