unit triangular matrix

A unit triangular matrix is a triangular matrix with $1$ on the diagonal.
i.e.

A unit upper triangular matrix is of the form

 $\begin{bmatrix}1&a_{12}&a_{13}&\cdots&a_{1n}\\ 0&1&a_{23}&\cdots&a_{2n}\\ 0&0&1&\cdots&a_{3n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ 0&0&0&\cdots&1\end{bmatrix}$

and is sometimes called a unit right triangular matrix.

A unit lower triangular matrix is of the form

 $\begin{bmatrix}1&0&0&\cdots&0\\ a_{21}&1&0&\cdots&0\\ a_{31}&a_{32}&1&\cdots&0\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&a_{n3}&\cdots&1\end{bmatrix}$

and is sometimes called a unit left triangular matrix.

Title unit triangular matrix UnitTriangularMatrix 2013-03-22 13:41:58 2013-03-22 13:41:58 Daume (40) Daume (40) 6 Daume (40) Definition msc 15-00 unit left triangular matrix unit right triangular matrix unit upper triangular matrix unit lower triangular matrix