Orthogonality

Given two elements $v$ and $w$ of a space equipped with a Scalar product $(v,w)$, the two elements are said to be orthogonal or perpendicular if their scalar product is zero, that is

Typically, the space in question is a Vector space and its elements are vectors. A more advanced definition is the orthogonality of two functions belonging to an infinite-dimensional space, such as a Hilbert space.