= Orthogonal similarity
{title2=$B=Q^TAQ,\quad Q^TQ=I$}
= Orthogonally similar
{synonym}
= Orthogonal similarity transformation
{synonym}
An orthogonal <matrix similarity> changes coordinates by an <orthogonal matrix>. It preserves <eigenvalues>, <singular values> and Euclidean geometry; it also preserves symmetry when applied to a <symmetric matrix>. A sequence of <Householder transformations> can use this freedom to produce a <Hessenberg reduction>, while a symmetric matrix can be reduced further to tridiagonal form.
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