# 4. Vector spaces

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.

### Contributors

- Isaiah Lankham, Mathematics Department at UC Davis
- Bruno Nachtergaele, Mathematics Department at UC Davis
- Anne Schilling, Mathematics Department at UC Davis

Both hardbound and softbound versions of this textbook are available online at WorldScientific.com.