Definition:Determinant/Matrix/Order 3/Summation Convention

From ProofWiki
Jump to navigation Jump to search


The determinant of a square matrix of order $3$ $\mathbf A$ can be expressed using the summation convention as:

$\det \left({\mathbf A}\right) = \dfrac 1 6 \operatorname{sgn} \left({i, j, k}\right) \operatorname{sgn} \left({r, s, t}\right) a_{i r} a_{j s} a_{k t}$

Note that there are six indices which appear twice, and so six summations are assumed.