Simple polynomial equations over (m x m)-matrices
[EN] Let m be any integer ? 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O,over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ? ? for each i and n ? 1. We discuss its solution set S supplied with the natural Euclidean topolog...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:dnet:riunet______::3f1b72f56eac4cc1dde1967325c8dc78 |
| Online Access: | https://riunet.upv.es/handle/10251/235812 |
| Access Level: | Open access |
| Keyword: | Polynomial equations over matrices Matrix algebra Covering dimension |
| Summary: | [EN] Let m be any integer ? 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O,over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ? ? for each i and n ? 1. We discuss its solution set S supplied with the natural Euclidean topology.In particular, we describe the solution set S for m=3 and calculate its dimension. |
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