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 non-zero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form an orthogonal basis.

The concept has been used in the context of orthogonal functions, orthogonal polynomials, and combinatorics.