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Consider an $N$ dimensional tensor $T$ using the strided view representation used by PyTorch, i.e. we have a storage vector $S$ projected into $N$ dimensions using a size tuple $s$ and a stride tuple $...

Given an $n$-mode tensor $\mathcal{T}\in\mathbb{R}^{d_1\times\dotsb\times d_n}$, there exists a Tucker decomposition of $\mathcal T$ of the form $$\mathcal{T} = \mathcal{X}\times_1 W_1\times_2\dotsb\...

Let us consider a matrix $M^{(a)}$ of size $N \times N$, having $N$ eigenvalues $\lambda_i \in \mathbb{C}$. Considering a rank-3 tensor, we can informally think of it as a sequence of $N$ matrices $M^{...

Suppose $U,V,W$ are the cyclotomic fields $\mathbb{Q}(\zeta_{m_3})$, $\mathbb{Q}_(\zeta_{m_2})$, and $\mathbb{Q}(\zeta_{m_1})$ respectively, where $m_1 \mid m_2 \mid m_3$ so that $U/V/W$ is a tower of ...

Hi I know how to calculate some easy tensor products like $\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}} \mathbb{Z}/n\mathbb{Z}\cong_{\mathbb{Z}} \mathbb{Z}/(m,n)\mathbb{Z} $ or $F[X] \otimes_{F} F[Y] \...