Elementary matrix transformations: Difference between revisions

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===3. Linear combinator transformations===

This transformation, ''T_ij(m)'', substractssubtracts row i multiplied by ''m'' from row j. The matrix resulting in this transformation is:<br>

:<math>

T_{i,j}(m) = \begin{bmatrix} 1 & & & & & & & \\ & \ddots & & & & & & \\ & & 1 & & & & & \\ & & & \ddots & & & & \\ & & -m & & 1 & & \\ & & & & & & \ddots & \\ & & & & & & & 1\end{bmatrix}