Abstract
Abstract In this paper, a space called geometric space, involving both the notions of area and length, is introduced in general setting. The interplay, between these two ideas, is studied. As a result, a new notion of orthogonality, called area-length orthogonality or A-L orthogonality, is demonstrated. It is shown that A-L orthogonality coincides with the standard notion of orthogonality for inner product spaces. Finally, it is proved that A-L orthogonality implies Birkhoff orthogonality, but not conversely.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have