          # Orthogonality

• the line segments ab and cd are orthogonal to each other.

in mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. two elements u and v of a vector space with bilinear form b are orthogonal when b(u, v) = 0. depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. in the case of function spaces, families of orthogonal functions are used to form a basis.

by extension, orthogonality is also used to refer to the separation of specific features of a system. the term also has specialized meanings in other fields including art and chemistry.

• etymology
• mathematics and physics
• art
• computer science
• communications
• statistics, econometrics, and economics
• taxonomy
• combinatorics
• chemistry and biochemistry
• system reliability
• neuroscience
• gaming
• other examples
## "Orthogonal" redirects here. For the trilogy of novels by Greg Egan, see Orthogonal (novel). For software design concept, see Orthogonality (programming). The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0. Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. Contents 1 Etymology 2 Mathematics and physics 2.1 Definitions 2.2 Euclidean vector spaces 2.3 Orthogonal functions 2.4 Examples 2.4.1 Orthogonal polynomials 2.4.2 Orthogonal states in quantum mechanics 3 Art 4 Computer science 5 Communications 6 Statistics, econometrics, and economics 7 Taxonomy 8 Combinatorics 9 Chemistry and biochemistry 10 System reliability 11 Neuroscience 12 Gaming 13 Other examples 14 See also 15 References 16 Further reading  