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As a side note, an '''unreduced''' symmetric tridiagonal matrix is a matrix containing non-zero off-diagonal elements of the tridiagonal, where the eigenvalues are distinct while the eigenvectors are unique up to a scale factor and are mutually orthogonal.<ref>{{cite book |last1=Dhillon |first1=Inderjit Singh |title=A New O(n 2 ) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem |page=8 |url=http://www.cs.utexas.edu/~inderjit/public_papers/thesis.pdf}}</ref>
For ''unsymmetric'' tridiagonal matrices one can compute the eigendecomposition using a [[Tridiagonal_matrix#Similarity_to_symmetric_tridiagonal_matrix|similarity transformation]].
=== Similarity to symmetric tridiagonal matrix ===
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