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Chapter 5 The Dimension of a Vector Space
Thus far in this text, the only way we have related vector spaces to each other is through linear transformations between those spaces. But we have not had any
intrinsic quality of a vector space that enables comparison between spaces.
The notion of the
dimension of a vector space allows just such a comparison. In this chapter we will develop the necessary machinery for defining dimension, and we will relate this concept to matrices, linear transformations, and more.
