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I just realized when I do linear transformation, for instance, rotating a Vector counter-clockwise by 90 degrees, then projecting it on the X2 axis. For each step, I need to multiply transforming Matrix to the left-hand side of the original Vector x. Why are the multiplications always on the left-hand side？ Under what circumstances, do we need to multiply these transforming matrices on the right-hand side?

Many thanks David

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  • $\begingroup$ First of all, you cannot multiply a let say $(2 \times 2)$-matrix on a $(2 \times 1)$-vector from the right; such a multiplication is not well-defined. $\endgroup$
    – Maty Mangoo
    Mar 14 at 23:45

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