# 4-vectors and tensor algebra

1. Jul 14, 2009

### smithg86

How would you write the following using index-notation?

$$s \cdot F \cdot u$$

Given that $$s = (s^0, \vec{s})$$ and $$u = \gamma(1, \vec{v})$$ are 4-vectors;
$$F$$ is a skew tensor of components $$F^{ik}$$ indicated as $$F = - ( \vec{F}^t, \vec{F}^s )$$, $$\vec{F}^t= \left\{F^{0 \alpha}\right\}$$, $$\vec{F}^s = \left\{F^{\beta \gamma}\right\}$$, with $$\alpha, \beta, \gamma = 1,2,3$$;
the dot between symbols indicates a contraction of neighboring indices with the metric tensor (+ ---).