All Questions

Let $[x]_{q}=\frac{1-q^x}{1-q}$ and $\binom{x}{n}_{q}$ denote a $q$-binomial coefficient. Let $A_n(x,q)$ be the $n\times n $ matrix with entries $$q^\binom{i-j}{2}\binom{i+j+x}{i-j+1}_{q},$$ $0 \le i,...

A matrix of real numbers is called totally positive if all its minors are non-negative. A well-known example is the Pascal matrix $(\binom{i}{j})$. Is it true that the minors of the $q$-Pascal matrix ...

I am a fan of the Matrix exponential $\exp(X)$, defined for any complex matrix $X$ by \begin{equation*} \exp(X) := \sum_{k \ge 0} \frac{X^k}{k!}. \end{equation*} I have a fleeting acquaintance with ...