Abstract
In this chapter, the reader is introduced with bilinear transformation, also called Möbious tranformation, which deals with more general situations in which we shall answer more abstract questions for determining whether and in what manner a given finite portion of an analytic surface could be represented on a portion of a plane. This chapter also deals with fixed points of bilinear transformations, elliptic, hyperbolic, and parabolic transformations along with some special bilinear transformations.
In mathematics the art of proposing a question must
be held of higher value than solving it
Georg Cantor
With my full philosophical rucksack I can only climb
slowly up the mountain of mathematics
Ludwig Wittgenstein, Culture and Value
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Notes
- 1.
This transformation is sometimes called Möbius transformation after A. F. Möbius (1790–1969) who first studied the same.
- 2.
This classification of bilinear transformation is due to Klein.
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Pathak, H.K. (2019). Bilinear Transformations and Applications. In: Complex Analysis and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-13-9734-9_6
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DOI: https://doi.org/10.1007/978-981-13-9734-9_6
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