Chapter 9: Matrix Decompositions and Beyond. In the chapter mind map this icon labels Tensors: Tensor Train (TT) & CP Decomps. The discussion below is excerpted and lightly edited from § Tensor Train (TT) Decomposition in Mathematics for AI and Machine Learning.

For a $d$-dimensional tensor $\mathcal{A} \in \mathbb{R}^{n_1 \times n_2 \times \cdots \times n_d}$, the Tensor Train (TT) decomposition represents it as a chain of low-rank core tensors:

where $\mathcal{G}_k$ are core tensors with ranks $R_k \ll n_k$. The storage requirement is $O(dnR^2)$ instead of $O(n^d)$, providing exponential compression for high-dimensional tensors.