Category:Examples of Determinants

This category contains examples of determinants.

Let $\lambda: \N_{> 0} \to \N_{> 0}$ be a permutation on $\N_{>0}$.

The determinant of $\mathbf A$ is defined as:

$\ds \map \det {\mathbf A} := \sum_{\lambda} \paren {\map \sgn \lambda \prod_{k \mathop = 1}^n a_{k \map \lambda k} } = \sum_\lambda \map \sgn \lambda a_{1 \map \lambda 1} a_{2 \map \lambda 2} \cdots a_{n \map \lambda n}$

where:

the summation $\ds \sum_\lambda$ goes over all the $n!$ permutations of $\set {1, 2, \ldots, n}$

$\map \sgn \lambda$ is the sign of the permutation $\lambda$.