Triangular matrix: Difference between revisions

Revision as of 18:04, 18 July 2004

Revision as of 20:51, 18 July 2004

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A matrix ''L'' of the form

:<math> \mathbf{L}

\begin{pmatrix}

l_{1,1} & & & & 0 \\

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is called '''lower triangular matrix'''. If the diagonal entries in ''L'' are one

:<math> \mathbf{L} =

\begin{pmatrix}

1 & & & & 0 \\

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the matrix is called '''unit lower triangular matrix''' or '''normed lower triangular matrix'''.

The matrix ''L''_i

:<math> \mathbf{L}_i =

\begin{pmatrix}

1 & & & & & 0 \\

& \ddots & & & & \\

& & 1 & & & \\

& & l_{i+1,i} & \ddots & & \\

& & \vdots & & \ddots & \\

0 & & l_{n,i} & 0 & & 1 \\

\end{pmatrix}

</math>

is called '''atomic''' lower triangular matrix.

Analogously a matrix ''U'' of the form

:<math> \mathbf{U} =

\begin{pmatrix}

u_{1,1} & u_{1,2} & u_{1,3} & \ldots & u_{1,m} \\

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is called '''upper triangular matrix'''. If the diagonal entries in ''U'' are one

:<math> \mathbf{U} =

\begin{pmatrix}

1 & u_{1,2} & u_{1,3} & \ldots & u_{1,m} \\