Definition:Tensor Rank

Definition

Let $F$ be a tensor of type $\tuple {l, k}$.

Then the tensor rank of $F$ is the sum $l + k$.

In other words, it is the total number of vectors and covectors it can act upon.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.): Appendix $\text B$. Review of Tensors