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Fashionable mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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How are families of orthogonal functions used in function spaces?
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.
When does an orthogonal interaction occur in chemistry?
In chemistry and biochemistry, an orthogonal interaction occurs when there are two pairs of substances and each substance can interact with their respective partner, but does not interact with either substance of the other pair.
How is the concept of orthogonality used in mathematics?
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. ... In the case of function spaces, families of orthogonal functions are used to form a basis.
When is a vector space with a bilinear form orthogonal?
A vector space with a bilinear form generalizes the case of an inner product. When the bilinear form applied to two vectors results in zero, then they are orthogonal. The case of a pseudo-Euclidean plane uses the term hyperbolic orthogonality. In the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ .
Last Update: Oct 2021
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