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Vector Spaces

Vector Spaces

A vector space V is a set of vectors that is closed under vector multiplication and addition. This means that vectors produced from vector addition and multiplication are also within the vector space:

  1. If a and b are vectors in the space V, then a + b is also in V.
  2. If c is a scalar and a and b are vectors in V, then ab and ac are also vectors inside V. When these properties hold true, the vector space is said to be "closed" under vector addition and scalar multiplication.

More Information:

  1. http://mathworld.wolfram.com/VectorSpace.html
  2. http://www.math.toronto.edu/gscott/WhatVS.pdf