Isosceles trapezoids, norms and inner products
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Generalizing a property of isosceles trapezoids in the real plane, we obtain a characterization of inner product spaces (i.p.s.). The same property allows us to give a definition of a new orthogonality relation, which is studied in detail and generalizes many of the well-known orthogonalities, e.g. Pythagoras, Birkhoff and James. This orthogonality has the property of being empty for 2 dimensional spaces, but we give some examples of 3 dimensional spaces, not i.p.s., that admit couples of vectors relationed by our orthogonality.
KeywordsDimensional Space Product Space Orthogonality Relation Real Plane Isosceles Trapezoid
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