3 problems

Let $A+iX+jY+kZ$ be a quaternion matrix, where $i^2=j^2=k^2=-1$ and $ijk=-1$, with real matrices $A,X,Y,Z$. Conjecture 29.7. The supplied statement asserts a formula for … but the…

Let $Z\in\mathbb{Q}^{n\times n}$ be a nonzero quaternion skew-symmetric matrix. For $n>2$, call $Z$ basic if there is no unitary matrix $U$ such that $UZU^*=\Sigma$, where $\Sigma$…

Applications conjecture. This simultaneous decomposition will also play an important role in signal processing and linear modelling.