PlanetMath: unit triangular matrix

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unit triangular matrix

(Definition)

A unit triangular matrix is a triangular matrix with on the diagonal.
i.e.

A unit upper triangular matrix is of the form

$\displaystyle \begin{bmatrix} 1 & a_{12} & a_{13} & \cdots & a_{1n} \ 0 & 1 &... ...s & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & 1 \end{bmatrix}$

and is sometimes called a unit right triangular matrix.

A unit lower triangular matrix is of the form

$\displaystyle \begin{bmatrix} 1 & 0 & 0 & \cdots & 0 \ a_{21} & 1 & 0 & \cdot... ...dots & \ddots & \vdots \ a_{n1} & a_{n2} & a_{n3} & \cdots & 1 \end{bmatrix}$

and is sometimes called a unit left triangular matrix.

"unit triangular matrix" is owned by Daume.

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Other names:

unit left triangular matrix, unit right triangular matrix

Also defines:

unit upper triangular matrix, unit lower triangular matrix

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Cross-references: diagonal, triangular matrix
There are 2 references to this entry.

This is version 3 of unit triangular matrix, born on 2003-06-17, modified 2006-06-21.
Object id is 4375, canonical name is UnitTriangularMatrix.
Accessed 8275 times total.

Classification:

AMS MSC:

15-00 (Linear and multilinear algebra; matrix theory :: General reference works )

Pending Errata and Addenda

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