Tridiagonal matrix

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 is tridiagonal:

${\displaystyle {\begin{pmatrix}1&4&0&0\\3&4&1&0\\0&2&3&4\\0&0&1&3\\\end{pmatrix}}.}$

The determinant of a tridiagonal matrix is given by the continuant of its elements.^[1]

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