Definition:Tridiagonal Matrix

Definition

A tridiagonal matrix is a matrix in which the elements outside the leading diagonal, the subdiagonal and the superdiagonal are all zero.

$\begin {pmatrix} a & b & 0 & \cdots & 0 & 0 \\ c & d & e & \cdots & 0 & 0 \\ 0 & f & g & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \cdots & w & x \\ 0 & 0 & 0 & \cdots & y & z \end {pmatrix}$

Also see

• Results about tridiagonal matrices can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): band matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): band matrix