strictly upper triangular matrix

A strictly is an upper triangular matrix which has $0$ on the main diagonal. Similarly a strictly lower triangular matrix is a lower triangular matrix which has $0$ on the main diagonal. i.e.

A strictly upper triangular matrix is of the form

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

A strictly lower triangular matrix is of the form

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