Editing Tridiagonal matrix (section)

{{Short description|Matrix with nonzero elements on the main diagonal and the diagonals above and below it}}
In [[linear algebra]], a '''tridiagonal matrix''' is a [[band matrix]] that has nonzero elements only on the [[main diagonal]], the subdiagonal/lower diagonal (the first diagonal below this), and the supradiagonal/upper diagonal (the first diagonal above the main diagonal). For example, the following [[matrix (mathematics)|matrix]] is [[Tridiagonal matrix algorithm|tridiagonal]]:
:<math>\begin{pmatrix}
1 & 4 & 0 & 0 \\
3 & 4 & 1 & 0 \\
0 & 2 & 3 & 4 \\
0 & 0 & 1 & 3 \\
\end{pmatrix}.</math>

The [[determinant]] of a tridiagonal matrix is given by the ''[[Continuant (mathematics)|continuant]]'' of its elements.<ref>{{cite book | author=Thomas Muir | author-link=Thomas Muir (mathematician) | title=A treatise on the theory of determinants | url=https://archive.org/details/treatiseontheory0000muir | url-access=registration | year=1960 | publisher=[[Dover Publications]] | pages=[https://archive.org/details/treatiseontheory0000muir/page/516 516–525] }}</ref>

An [[orthogonal transformation]] of a symmetric (or Hermitian) matrix to tridiagonal form can be done with the [[Lanczos algorithm]].