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- Title
APPROXIMATELY ANGLE PRESERVING MAPPINGS.
- Authors
MOSLEHIAN, MOHAMMAD SAL; ZAMANI, ALI; WÓJCIK, PAWEŁ
- Abstract
We study linear mappings which preserve vectors at a specific angle. We introduce the concept of $(\unicode[STIX]{x1D700},c)$ -angle preserving mappings and define $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ as the 'smallest' number $\unicode[STIX]{x1D700}$ for which $T$ is an $(\unicode[STIX]{x1D700},c)$ -angle preserving mapping. We derive an exact formula for $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ in terms of the norm $\Vert T\Vert$ and the minimum modulus $[T]$ of $T$. Finally, we characterise approximately angle preserving mappings.
- Subjects
MATHEMATICAL mappings; ISOMETRICS (Mathematics); APPROXIMATION theory; SIMILARITY (Geometry); VECTORS (Calculus)
- Publication
Bulletin of the Australian Mathematical Society, 2019, Vol 99, Issue 3, p485
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972718001430