Tag Archives: determinants

Determinants, Permutations and the Lie Algebra of SL(n)

Here is an old classic from linear algebra: given an $n\times n$ matrix $A = (a_{ij})$, the determinant of $A$ can be calculated using the permuation formula for the determinant: $\det(A) = \sum_{\sigma\in S_n} (-1)^\sigma a_{1\sigma(1)}\cdots a_{n\sigma(n)}$. Here $S_n$ denotes the permutation group on $n$ symbols and $(-1)^\sigma$ […]