Orthogonality and Mathematical Physics

The present work shows how the notion of perpendicularity introduced and applied by Euclid in his “Elements” in the 3rd century BC for which the sign “⊥” has been used since 1634 firstly by the French mathematician Pierre Hérigone in one of his books can be extended in Functional Analysis under the name of orthogonality and how it can be applied in mathematical Physics. Knowledge in mathematical Analysis and functional Analysis are applied along the book. A special role is played by compact operators applied in solving operatorial (integral) equations.