6. Tensor Algebra

6.1. Basis

Definition 6.1 (Basis)

Definition 6.2 (Reciprocal basis)

In a inner product space, the reciprocal basis of a given basis \(\{ \vec{b}_a \}_{a=1:d}\) is the set of vectors \(\{ \vec{b}_{b} \}_{b=1:d}\), s.t.

\[\vec{b}^b \cdot \vec{b}_a = \delta_a^b \ .\]

6.2. Exterior algebra

\[\land\]

6.3. Exterior product

Generalization of the vector product