# 8: Permutations and the Determinant

- Page ID
- 284

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There are many operations that can be applied to a square matrix. This chapter is devoted to one particularly important operation called the **determinant**. In effect, the determinant can be thought of as a single number that is used to check for many of the different properties that a matrix might possess. In order to define the determinant operation, we will ﬁrst need to define permutations.

- 8.1: Permutations
- Permutations appear in many different mathematical concepts, and so we give a general introduction to them in this section.

- 8.2: Determinants
- Now that we have developed the appropriate background material on permutations, we are finally ready to define the determinant and explore its many important properties.

## 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.