All Questions

Define an antisymmetric 1-x-matrix as an $n\times n$ matrix $M=(m_{ij})$ with $m_{ii}=0$ and $\{m_{ij},m_{ji}\}=\{1,x\}$ for all $1\le i<j\le n$. Call their set $\mathcal A_n$. The setup is as ...

Define $\mathcal M_n$ as the set of all $n\times n$ matrices of full rank with each entry either 1 or $x$. I am interested in how big the determinant of such a matrix can be. For this, we define in a ...

How many distinct rows and columns a real square matrix can have (at least in symmetric case) such that rank of matrix is $r$ and entries: are from $\{-b,-b+1,\dots,0,\dots,b-1,b\}$? are from $\{-b,-...

Consider families of $0/1$ matrices in $\Bbb B$ where $1+1=1$: $\mathcal M_{1,n,c}$ contains $2^n\times 2^n$ matrices that can be written as Hadamard product of $t=O(2^{(\log n)^c})$ matrices $$(J_n-...

Let $\mathscr{M}[n]$ be collection of $n\times n$ matrices with real entries from $\{0,1\}$ such that every row is distinct and every column is distinct. What is minimum real rank of matrices in $\...