About: Orthonormal set

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A set of vectors is called a orthonormal set if all vectors are orthogonal to every vector in the set and are all unit vectors. Mathematically, this is stated as where is the Kronecker delta function and is the inner product (which can also be extended to real functions; as such a set of functions can be orthonormal). The span of the set forms an orthonormal basis. An example of this is Cartesian coordinates. A matrix whose columns form an orthonormal set is called an orthogonal matrix, and will have the property

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rdfs:label	Orthonormal set
rdfs:comment	A set of vectors is called a orthonormal set if all vectors are orthogonal to every vector in the set and are all unit vectors. Mathematically, this is stated as where is the Kronecker delta function and is the inner product (which can also be extended to real functions; as such a set of functions can be orthonormal). The span of the set forms an orthonormal basis. An example of this is Cartesian coordinates. A matrix whose columns form an orthonormal set is called an orthogonal matrix, and will have the property
dcterms:subject	Linear algebra
dbkwik:math/proper...iPageUsesTemplate	dbkwik:resource/YQ6zjeEdBknZVKEvXc8BGQ==
abstract	A set of vectors is called a orthonormal set if all vectors are orthogonal to every vector in the set and are all unit vectors. Mathematically, this is stated as where is the Kronecker delta function and is the inner product (which can also be extended to real functions; as such a set of functions can be orthonormal). The span of the set forms an orthonormal basis. An example of this is Cartesian coordinates. A matrix whose columns form an orthonormal set is called an orthogonal matrix, and will have the property where is the inverse of and is its transpose. Real orthogonal matrices will have a determinant of either 1 or -1. An extension to complex matrices is a matrix whose inverse is equal to its conjugate transpose, and is called a unitary matrix. File:Linear subspaces with shading.svg This linear algebra-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.

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