Editing Tridiagonal matrix (section)

==Computer programming==
A transformation that reduces a general matrix to Hessenberg form will reduce a Hermitian matrix to tridiagonal form.  So, many [[eigenvalue algorithm]]s, when applied to a Hermitian matrix, reduce the input Hermitian matrix to (symmetric real) tridiagonal form as a first step.<ref>{{Cite journal |last1=Eidelman |first1=Yuli |last2=Gohberg |first2=Israel |last3=Gemignani |first3=Luca |date=2007-01-01 |title=On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms |journal=Linear Algebra and Its Applications |language=en |volume=420 |issue=1 |pages=86–101 |doi=10.1016/j.laa.2006.06.028 |issn=0024-3795|doi-access=free }}</ref>

A tridiagonal matrix can also be stored more efficiently than a general matrix by using a special [[matrix representation|storage scheme]]. For instance, the [[LAPACK]] [[Fortran]] package stores an unsymmetric tridiagonal matrix of order ''n'' in three one-dimensional arrays, one of length ''n'' containing the diagonal elements, and two of length ''n'' &minus; 1 containing the [[subdiagonal]] and [[superdiagonal]] elements.