Can anybody show how to prove or show where to find a proof of the following statement:
Given a matrix $T = \begin{pmatrix} t_{11} & 0 & 0 & \dotsm & 0 & 0& \dotsm & 0& 0\\ t_{21} & t_{22} & 0 & \dotsm & 0 & 0& \dotsm & 0 & 0 \\ 0 & t_{32} & t_{33} & \dotsm & 0& 0& \dotsm & 0 & 0 \\ \vdots \\0 & 0 & 0 & \dotsm & t_{i,i-1} & t_{ii} & \dotsm &0&0 \\ \vdots \\0&0&0& \dotsm &0& 0 & \dotsm &t_{m,m-1}&t_{mm} \end{pmatrix}$ where $0 \leqslant t_{ij} \leqslant 1$ ( for $ 1 \leqslant i,j \leqslant m , i \neq j), 0