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Is it possible to find matrix solutions to the following : $$\left(\sum_1^m M_k x_k\right)^n=\left(\sum_1^m x_k^n\right)I_d$$ where $M_k$ are the desired $d \times d$ matrices (no restriction on $d$) …

How to study the decomposition of a square matrix into a product of sparse matrices? There are no restrictions on the number of matrices in the product, but the fewer the better.

I am trying to characterize matrices with a certain property : Define $U$ as an $n \times n$ matrix (over C or R; you can also assume that it is unitary or orthogonal if it helps). Now take $n$ unknow …

I have a $k \times n$ matrix $G$ over ${\mathbb F_2}$ that's full rank. This can always be put in systematic form : $G \sim [I_k \mid P]$ where $I_k$ is a $k \times k$ identity matrix and $P$ is a $k …

I don't have Lawson and Michelson's "Spin Geometry'" but this presentation looks like that of the extraspecial group of order 2^{2n+1} which is a subgroup of the Clifford group.

In a previous post Lift chain complex from $\mathbb{F}_2$ to $\mathbb{Z}$ the body of the question mentions that this (lifting a chain complex from $\mathbb Z/2\mathbb Z$ to $\mathbb Z$) is always pos …