All Questions

Let $k\ge2$. The maximum number of $0$-$1$ (column) vectors of length $2k-1$ which make a rank $k$ matrix with no zero row nor two identical rows is $2^{k-1}+1$. (The rank is over the rationals.) I ...

Let $\text{Mat}(n\times n,\mathbb{Z})$ denote the collection of integer $n\times n$ matrices. We say $M\in \text{Mat}(n\times n,\mathbb{Z})$ is a power matrix if there is an integer $k>1$ and a ...

I have the following question: Is there a closed formula for the elementary divisors of the Matrix $M=\lbrace (m_{ij})\rbrace_{i=1,...,n,\ j=1,...,k}$, where $m_{ij}$ is the greatest common ...

Hello everybody ! I was reading a book on geometry which taught me that one could compute the volume of a simplex through the determinant of a matrix, and I thought (I'm becoming a worse computer ...