Determinant/Examples/Order 3/Einstein Summation Convention

Definition

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

$\map \det {\mathbf A} = \dfrac 1 6 \map \sgn {i, j, k} \map \sgn {r, s, t} a_{i r} a_{j s} a_{k t}$

Note that there are $6$ indices which appear twice, and so $6$ summations are assumed.

Sources

• 1980: A.J.M. Spencer: Continuum Mechanics ... (previous) ... (next): $2.2$: The summation convention: $(2.14)$