Matrix Determinants

Why

Let $A \in R^{d \times d}$ where $R$ is a ring. The determinant of $A$ is

\[ \sum_{\sigma \in S_n} \left( \sgn(\sigma ) \prod_{i = 1}^{n} a_{i,\sigma _{i}} \right) \]

We denote the determinant of $A$ by $\det A$.

Future editions will include, and will probably take the genetic approach via volumes in three-dimensional space. ↩︎