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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.
‘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.’
‘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.’
‘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.’
‘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.’