: How does a matrix equation increases speed of system ?
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If you have to apply a bunch of linear transformations repeatedly, you can represent them in a matrix. That in itself doesn’t make the math any faster, but the next thing you can (usually) do is diagonalize the matrix. Now you can apply the transformation as many times as you want, for more or less the same amount of computations as applying and inverting the diagonalization, which is just two matrix multiplications (once you know the diagonalization for it).
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