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- W1639969081 abstract "In this document we study the local connectivity of the sets whose elements are $m$-tuples of pairwise commuting normal matrix contractions. Given $varepsilon>0$, we prove that there is $delta>0$ such that for any two $m$-tuples of pairwise commuting normal matrix contractions $mathbf{X}:=(X_1,ldots,X_m)$ and $tilde{mathbf{X}}:=(tilde{X}_1,ldots,tilde{X}_m)$ that are $delta$-close with respect to some suitable distance $ð$ in $(mathbb{C}^{ntimes n})^m$, we can find a $m$-tuple of matrix paths (homotopies) connecting $mathbf{X}$ to $mathbf{tilde{X}}$ relative to the intersection of some $varepsilon,ð$-neighborhood of $mathbf{X}$ with the set of $m$-tuples of pairwise commuting normal matrix contractions. One of the key features of these matrix homotopies is that $delta$ can be chosen independent of $n$. Some connections with topology and numerical matrix analysis will be outlined as well." @default.
- W1639969081 created "2016-06-24" @default.
- W1639969081 creator A5083296095 @default.
- W1639969081 date "2015-06-24" @default.
- W1639969081 modified "2023-09-27" @default.
- W1639969081 title "Dynamical Deformation of Toroidal Matrix Varieties" @default.
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