Real Matrix Determinants
Definition
Given a square matrix $A \in \R ^{n \times
n}$.
\[
\sum_{\sigma \in S_n} \left( \sgn(\sigma ) \prod_{i = 1}^{n}
a_{i,\sigma _{i}} \right)
\]
Given a square matrix $A \in \R ^{n \times
n}$.
\[
\sum_{\sigma \in S_n} \left( \sgn(\sigma ) \prod_{i = 1}^{n}
a_{i,\sigma _{i}} \right)
\]