Linear Space 283 浏览 0关注

A vector space is a mathematical structure formed by a collection of Element (mathematics)|elements called vectors, which may be Vector addition|added together and Scalar multiplication|multiplied (scaled) by numbers, called scalar (mathematics)|scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field (mathematics)|field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed #Definition|below. An example of a vector space is that of Euclidean vectors, which may be used to represent physics|physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometry|geometric sense, vectors representing displacements in the plane or in...
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