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.