Triangular matrix: Difference between revisions

Revision as of 20:26, 29 May 2005

Revision as of 21:17, 25 June 2005

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is called '''upper triangular matrix''' or '''right triangular matrix'''.

A triangular matrix with zero entries on the [[main diagonal]] is '''strictly''' upper or lower triangular. All strictly triagulartriangular matrices are [[nilpotent matrix|nilpotent]].

If the entries on the main diagonal are 1, the matrix is termed '''unit''' upper/lower or '''normed''' upper/lower triangular. If, in addition, all the off-diagonal entries are zero except for the entries in one column, then the matrix is '''atomic''' upper/lower triangular; such a matrix is also called a '''Gauss (transformation) matrix'''. So an atomic lower triangular matrix is of the form

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\end{bmatrix}.

</math>

The inverse of an atomic triagulartriangular matrix is again atomic triangular. Indeed, we have

:<math> \mathbf{L}_{i}^{-1} =

\begin{bmatrix}