# Notation for tensors of rank 3 and higher

A tensor of rank 2 is often denoted $$\bar{\bar{D}}$$. What is the notation for higher-ranked tensors?

• I think the best is to just say in words: $T$ is a tensor of type $(r,s)$ over the vector space $V$. Or in symbols, $T \in T^r_s(V)$. May 23, 2020 at 20:32

A rank 2 tensor is a matrix. In my own (handwritten) work, I denote a vector with a single underline ($$\underline{v}$$), a matrix with a double underline ($$\underline{\underline{M}}$$) and a tensor (rank 3 or higher) with a rectangle underneath [EDIT: have been alerted that this is indeed possible and looks like this: $$\underset{\square}T$$] or perhaps bold unitalicized ($$\mathit{\mathbf{T}}$$). This is assuming I need to reference all three kinds of objects at once. However, if I am only talking about matrices, or only talking about vectors, or only talking abou tensors, I might simply use boldface, like in my answer to this post about vectors or this post about matrices. In short, there is no universally accepted standard, but you should do your best to make it clear.
• $\underset{\square}{T}$ is \underset{\square}{T} May 24, 2020 at 4:59