Definition:Bidiagonal Matrix/Upper

Definition

An upper bidiagonal matrix is a square matrix in which the elements outside the leading diagonal and superdiagonal are all zero.

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

That is, a square matrix such that $a_{i j} = 0$ when $i > j$ or $j > i + 1$.

Also see

• Definition:Lower Bidiagonal Matrix

• Results about bidiagonal matrices can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bidiagonal matrix