Triangular matrix: Difference between revisions

Revision as of 23:14, 21 April 2005

Revision as of 22:45, 22 April 2005

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

IfA thetriangular matrix with zero entries on the [[principalmain diagonal]] is '''strictly''' upper or lower triangular. All strictly triagular 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

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

\begin{bmatrix}