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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
Large scale analysis of matrix multiplications
If $m,n \to \infty$ with $\frac{m}n \to \lambda \in (0,\infty)$ (let's suppose that $n$ depends on $m \in\mathbb{N}$), and if you are saying that each $\mathbf{B} = \mathbf{B}_m$ is an $m\times n$ ran …
9
votes
2
answers
233
views
Matrix invariants for simultaneous conjugation by a finite subgroup of $\textrm{GL}_n$
Let $K$ be a field of characteristic 0, and consider $d$ generic $n\times n$ matrices $X_1,\ldots,X_d$ where $X_k = (x_{ijk})_{ij}$ and $ K[x_{ijk}]$ is the polynomial algebra in $n^2 \cdot d$ variabl …