Now I have a matrix $\begin{equation}\label{key} R = \begin{bmatrix} 0 & 0 & \cdots & 0 & \\ 1 & 1 & \cdots & 1 \\ 2a_1 & 2a_2 & \cdots & 2a_n \\ \vdots & \vdots & \ddots & \vdots \\ (T-2)a_1^{T-3} & (T-2)a_2^{T-3} & \cdots & (T-2)a_n^{T-3} \end{bmatrix} \end{equation}$, where $T = 2n+1$, and $\forall i, -1< a_i < 1$.
My question is how to give an upper bound on the minimum singular value of $R$.