Orthogonality is a term with various meanings depending on the context.

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity. Although many authors use the two terms perpendicular and orthogonal interchangeably, the term perpendicular is more specifically used for lines and planes that intersect to form a right angle, whereas orthogonal is used in generalizations, such as orthogonal vectors or orthogonal curves.

The term is also used in other fields like physics, art, computer science, statistics, and economics.

The word comes from the Ancient Greek ὀρθός (orthós), meaning "upright", and γωνία (gōnía), meaning "angle".

The Ancient Greek ὀρθογώνιον (orthogṓnion) and Classical Latin orthogonium originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word orthogonalis came to mean a right angle or something related to a right angle.

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to 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.