
# 4. Vector spaces

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$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

Now that important background has been developed, we are ﬁnally ready to begin the study of Linear Algebra by introducing vector spaces. To get a sense of how important vector spaces are, try ﬂipping to a random page in these notes. There is very little chance that you will ﬂip to a page that does not have at least one vector space on it.

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