8.8 Unit Lower-Triangular Matrix

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 8.7 Lower-Triangular Matrix

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Unit Lower-Triangular Matrix

A unit lower-triangular matrix $L \in R^{n \times n}$ is a 8.7 Lower-Triangular Matrix with $ℓ_{i k} = 0$ if $i = k$ . Unit lower-triangular matrices take the form

L = [\begin{matrix} 1 & 0 & \dots & 0 \\ ℓ_{21} & 1 & ⋱ & ⋮ \\ ⋮ & ⋱ & ⋱ & 0 \\ ℓ_{n 1} & ℓ_{n 2} & \dots & 1 \end{matrix}]

Remark. This is called a gaussian elimination.
$⧫$