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APPROXIMATELY ANGLE PRESERVING MAPPINGS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 3 / June 2019
- Published online by Cambridge University Press:
- 14 February 2019, pp. 485-496
- Print publication:
- June 2019
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- Article
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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.
