Orthogonal matrix: Difference between revisions

 

==Overview==

 

An orthogonal matrix is the real specialization of a unitary matrix, and thus always a [[normal matrix]]. Although we consider only real matrices here, the definition can be used for matrices with entries from any [[field (mathematics)|field]]. However, orthogonal matrices arise naturally from [[dot product]]s, and for matrices of complex numbers that leads instead to the unitary requirement. Orthogonal matrices preserve the dot product,<ref>[http://tutorial.math.lamar.edu/Classes/LinAlg/OrthogonalMatrix.aspx "Paul's online math notes"]{{Citation broken|date=January 2013|note=See talk page.}}, Paul Dawkins, [[Lamar University]], 2008. Theorem 3(c)</ref> so, for vectors {{math|'''u'''}} and {{math|'''v'''}} in an {{mvar|n}}-dimensional real [[Euclidean space]]