TY - JOUR
A2 - Gilányi, Attila
AU - Greensite, Fred
PY - 2012
DA - 2012/08/01
TI - A New Proof of the Pythagorean Theorem and Its Application to Element Decompositions in Topological Algebras
SP - 353917
VL - 2012
AB - We present a new proof of the Pythagorean theorem which suggests a particular decomposition of the elements of a topological algebra in terms of an “inverse norm” (addressing unital algebraic structure rather than simply vector space structure). One consequence is the unification of Euclidean norm, Minkowski norm, geometric mean, and determinant, as expressions of this entity in the context of different algebras.
SN - 0161-1712
UR - https://doi.org/10.1155/2012/353917
DO - 10.1155/2012/353917
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi Publishing Corporation
KW -
ER -