Definition of vector space in US English:

vector space


  • A space consisting of vectors, together with the associative and commutative operation of addition of vectors, and the associative and distributive operation of multiplication of vectors by scalars.

    • ‘A succession of such elementary processes forms an evolutionary tree, which can be represented in the multidimensional vector space’
    • ‘Hilbert spaces, a special type of vector space, form the basis for the whole of quantum mechanics.’
    • ‘Students attending such a course are expected to know, from previous courses, that an inner-product space is a vector space equipped with an inner product, and that a space is complete if every Cauchy sequence in it converges.’
    • ‘This book contains the first definition of a vector space given with a remarkably modern notation and style and, although it was not appreciated by many at the time, this is surely a quite remarkable achievement by Peano.’
    • ‘The applications of the theory… to problems in classical algebra and analysis show how much can be done without ever defining a normed vector space, a Banach space or a Hilbert space.’