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$\DeclareMathOperator\GL{GL}$Let $X$, $Y$, $Z$ be $\mathbb{C}$-vector spaces, and let $A\subseteq X$ and $B\subseteq Y$ and $C\subseteq Z$ be linear subspaces. Let $V=X \otimes Y \otimes Z$, acted on ...

Consider $T_1 \in \mathbb{C}^{d_1 \times \cdots \times d_k}$ as an order-$k$ tensor of the format $(d_1, \cdots , d_k)$. Now, let $T_2$ be an unfolding of $T_1$ that is obtained by merging $\mathbb{C}^...

I have a matrix $M\in\mathbb{R}^{n\times k}$, with $k<n$ whose columns $m_i$ are linearly independent. So we have $M := [m_1|..|m_k]$. From the columns of $M$ I can define the following matrix $$ ...

Let $G=Gr(2,6)$ the Grassmannian of two planes in $V=\mathbb C^6$, and let $\mathcal Q(1)$ the rank four quotient bundle on it twisted with $\mathcal O_G(1) \cong $ det$(S^*)$, $S$ being the ...

I am trying to understand the space of all orthogonal tensors, I asked a more general version of this question here but with no solution yet found. I want to look at the simplest case first, namely a $...