On matrices for which norm bounds are attained
| dc.creator | Schneider, Hans | |
| dc.creator | Weinberger, Hans F. | |
| dc.date | 1998-03-13 | |
| dc.date.accessioned | 2026-07-07T05:24:05Z | |
| dc.date.available | 2026-07-07T05:24:05Z | |
| dc.description | Let $\|A\|_{p,q}$ be the norm induced on the matrix $A$ with $n$ rows and $m$ columns by the Hölder $\ell_p$ and $\ell_q$ norms on $R^n$ and $R^m$ (or $C^n$ and $C^m$), respectively. It is easy to find an upper bound for the ratio $\|A\|_{r,s}/\|A\|_{p,q}$. In this paper we study the classes of matrices for which the upper bound is attained. We shall show that for fixed $A$, attainment of the bound depends only on the signs of $r-p$ and $s-q$. Various criteria depending on these signs are obtained. For the special case $p=q=2$, the set of all matrices for which the bound is attained is generated by means of singular value decompositions. | |
| dc.identifier | https://arxiv.org/abs/math/9803060 | |
| dc.identifier | http://arxiv.org/abs/math/9803060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76697 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 15A60, 15A18 | |
| dc.title | On matrices for which norm bounds are attained | |
| dc.type | text |