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What is the smallest number of rows one can delete from a matrix to reduce its rank (by $1$)? Is there any standard name / notation for this characteristic? Has it been studied? I am in fact ...

The maximal order of an element of $\mathrm{GL}(n,\mathbb{F}_q)$ is $q^n-1$, where the characteristic of $\mathbb{F}_q$ is odd $p$. See here for a nice proof that uses the Cayley-Hamilton Theorem. ...

I tried asking this question on Math StackExchange and didn't get any replies. I was hoping that maybe someone here could help, sorry for duplicating. I'm trying to figure out some properties of ...

Let $C = \{c \in \mathbb{F}^n_2 : Hc=0\}$ be a binary linear code where $H \in \mathbb{F}^{k \times n}_2$ is a block lower-triangular matrix of full rank called the parity-check matrix of $C$. Clearly ...