3 problems

Let $\beta$ denote the parameter governing the clustering scale, and suppose that for a general matrix $V$ the particles rapidly converge to a lower-dimensional subspace spanned by…

Let $Q$ and $K$ be arbitrary matrices, and let $V$ be a matrix whose largest eigenvalue $\lambda_{\max}>0$ is real, with eigenspace $L$ satisfying $\mathop{\rm dim} L\geq2$. Assume…

Let $Q$ and $K$ be arbitrary matrices, and let $V$ be diagonalizable with $d$ different positive real eigenvalues. Denote its largest eigenvalue by $\lambda_{\max}$, and let $\xi$…