Study on the Complex Angle in Normed Spaces

In complex normed vector spaces, we consider a generalised angle. Its definition is the same as the Euclidean angle definition in real inner product spaces. It’s unsurprising that it produces complex values like ‘angles.’ This ‘angle’ has a few basic features that may be deduced from the typical angle in real inner product spaces. Real angles are required to perform conventional Euclidean geometry. We show that there exist many pure real valued ‘angles’ even in a complex normed space. In the inner product spaces, the situation is still improving. There, we can apply the theory of orthogonal systems to identify many pairs of vectors with real angles, as well as to do geometry based on ideas that the Greeks knew 2000 years ago.

Author (s) Details

Volker W. Thürey
Hegelstr. 101, 28201 Bremen, Germany

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