Orthogonality (mathematics)

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms.

Two elements u and v of a vector space with bilinear form ${\displaystyle B}$ are orthogonal when ${\displaystyle B(\mathbf {u} ,\mathbf {v} )=0}$. Depending on the bilinear form, the vector space may contain null vectors, non-zero self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality.

In the case of function spaces, families of functions are used to form an orthogonal basis, such as in the contexts of orthogonal polynomials, orthogonal functions, and combinatorics.