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Given $n$ matrices $A_i \in \mathbb{Z}^{m\times m}$. I am interested in the ideal $I_d(A)$ generated by the $d\times d$-minors of $A = \sum_{i=1}^n x_iA_i \in \mathbb{Z}[x_1, \dots , x_n]$. The matrix ...

Let $L$ be a field with a field embedding $\sigma:L \rightarrow L$, and $K=L^{\sigma}$ be the fixed field of $\sigma$. For $A \in M_n(L)$ a matrix, consider the set $X=\{x \in L^n|Ax=\sigma(x) \}$ ...

Given an invertible square matrix $M$ with entries from some number field $K$ which is Galois over $\mathbb{Q}$, sum the Galois conjugates of $M$ to form a new matrix $M' = \Sigma_{\sigma \in \mathrm{...