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$\newcommand{\lrank}{\operatorname{lrank}}$ $\newcommand{\rank}{\operatorname{rank}}$ Given a matrix $A$, we can define its Hamming weight, $w(A)$, as the number of non-zero elements in it. Now, given ...

Mo-ers, Do you know how it was that the study of the Jordan canonical form began? There are certain things that may be said once one has thought about the matter: for instance, one can say that the ...

I am interested in block matrices $A$, that is $A\in M_{n\times n}(R)$ where $R=M_{s\times s}(k)$ and $k$ is a field, such that for every positive integer $m$ the matrix $A^m$ has only scalar blocks ...

My problem : I have a family of $4 \times 4$ symmetric matrices. More precisely consider an interger $d$, a real $\lambda> 0$ and define the family $S_{\lambda}$: $ \{A(\lambda,x_1,x_2) ; (x_1,...

Cross-posted at Math SE Let $S\subseteq M_{n,m}(\mathbb{C})$ be a $d$-dimensional subspace of the space of $n\times m$ complex matrices (with $n\leq m$, say). I am interested in figuring out ...