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I recently need to apply the following concept of product of two 2d tensors to create a 3d tensor (tensors understood as generalized arrays): given two 2d tensors $A_{m\times n}$ and $B_{n\times p}$, ...

Richard Hamilton "A matrix Harnack estimate for the heat equation. Communications in Analysis and Geometry. 1(1993), 113-126." On page 125, at the end of the proof of Theorem 4.3, I abstract ...

Consider a graph $G=(V,E)$. Its adjacency matrix $A$ is defined by $A_{u,v} = 1$ if $(u,v)\in E$, $0$ otherwise. Consider a vector $x$ that associates a value $x_v$ to each vertex of $G$. Consider the ...

My question is about rank-1 decomposability of symmetric tensors over the reals. Let $v_1,\dots,v_n\in\mathbb{R}^d$ be vectors. Construct the object: $$ V=\sum_{j=1}^n \underbrace{v_j\otimes v_j\...