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strictly upper triangular matrix (Definition)

A strictly upper triangular matrix is an upper triangular matrix which has 0 on the main diagonal. Similarly a strictly lower triangular matrix is a lower triangular matrix which has 0 on the main diagonal. i.e.

A strictly upper triangular matrix is of the form

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

A strictly lower triangular matrix is of the form

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



"strictly upper triangular matrix" is owned by Daume.
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Other names:  supertriangular
Also defines:  strictly lower triangular matrix

Attachments:
If $A \in M_n(R)$ and $A$ is supertriangular then $A^n=0$ (Theorem) by Daume
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Cross-references: lower triangular matrix, diagonal, upper triangular matrix, strictly
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This is version 5 of strictly upper triangular matrix, born on 2003-06-19, modified 2006-06-22.
Object id is 4381, canonical name is StrictUpperTriangularMatrix.
Accessed 6489 times total.

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