# 8: Permutations and the Determinant

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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.
• 8.E: Exercises for Chapter 8

## Contributors

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

This page titled 8: Permutations and the Determinant is shared under a not declared license and was authored, remixed, and/or curated by Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling.