More verbosely, we may say that an orthonormal set is a subset of an inner product space such that the following two conditions hold:
If and , then is orthogonal (http://planetmath.org/OrthogonalVector) to .
If , then the norm of is .
Stated this way, the origin of the term is clear: an orthonormal set of vectors is both orthogonal and normalized.
Note that the empty set is orthonormal, as is a set consisting of a single vector of unit norm in an inner product space.
|Date of creation||2013-03-22 12:07:24|
|Last modified on||2013-03-22 12:07:24|
|Last modified by||yark (2760)|