Consider a full-row rank matrix $A \in \mathbb{C}^{r \times n}$ (where the number of rows r is less than the number of columns n). How can we find a column permutation or an invertible transformation T such that TA has the following form: $\begin{bmatrix} C_{1,1} & \cdots & C_{1,j_1} & C_{1,j_1+1} & \cdots & C_{1,j_1+j_2} & C_{1,j_1+j_2+1} & \cdots & C_{1,j_1+j_2+j_3} & \cdots & C_{1,j_1+\cdots+j_{r-1}+1} & \cdots & C_{1,j_1+\cdots+j_r} \\ 0 & \cdots & 0 & C_{2,j_1+1} & \cdots & C_{2,j_1+j_2} & C_{2,j_1+j_2+1} & \cdots & C_{2,j_1+j_2+j_3} & \cdots & C_{2,j_1+\cdots+j_{r-1}+1} & \cdots & C_{2,j_1+\cdots+j_r} \\ 0 & \cdots & 0 & 0 & \cdots & 0 & C_{3,j_1+j_2+1} & \cdots & C_{3,j_1+j_2+j_3} & \cdots & C_{3,j_1+\cdots+j_{r-1}+1} & \cdots & C_{3,j_1+\cdots+j_r} \\ \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \\ 0 & \cdots & 0 & 0 & \cdots & 0 & 0 & \cdots & 0 & \cdots & C_{r,j_1+\cdots+j_{r-1}+1} & \cdots & C_{r,j_1+\cdots+j_r} \end{bmatrix} $ We aim to find such a transformation T so that the number of elements in the set $\{ j_1, j_2, \dots, j_r \} $that are greater than or equal to 2 is maximized.（QR decomposition with block sizes $\{ j_1, j_2, \dots, j_r \}=1$),please advise!
