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English source...
A real matrix is '''orthogonal''' (or, more precisely, '''orthonormal''') when it has an inverse equal to its transpose<ref name="frtext">[http://benhur.teluq.uqam.ca/SPIP/inf6104/article.php3?id_article=13 Vecteurs et matrices], at http://benhur.teluq.uqam.ca, in French</ref>:
A real matrix is '''orthogonal''' (or, more precisely, '''orthonormal''') when it has an inverse equal to its transpose<ref name="frtext">[http://benhur.teluq.uqam.ca/SPIP/inf6104/article.php3?id_article=13 Vecteurs et matrices], at http://benhur.teluq.uqam.ca, in French</ref><ref>[http://mathworld.wolfram.com/OrthogonalMatrix.html Rowland, Todd. "Orthogonal Matrix."] From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. </ref>
:''P''<sup>T</sup>=''P''<sup>-1</sup>
:''P''<sup>T</sup>=''P''<sup>-1</sup>