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.
- 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.
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