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How to select the location of submatrices to have specific property in the output of multiplication

Your condition is $W_{2,2} W_{2,2}^T = I$ $T = W_{2,2}^{-1} W_{2,1}$ If $T$ has non-zero elements only in the first collumn it means that $T = \begin{bmatrix} \textbf C & \textbf 0_{P \times (P-r)}...
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