Matrix multiplication is clearly defined but is there a tangible or physical interpretation for it? Or is it just abstract formalism?(adsbygoogle = window.adsbygoogle || []).push({});

I am thinking about each column of the matrix as vectors so matrix multiplication with two 2by2 matrices is about multiplying 4 vectors in a certain way. The result is a 2by2 matrix with all four vectors tangled up with each other. But does the two resultant vectors in this matrix have a meaning with respect to the original vectors if we gave the original vectors some meaning in the first place?

I do see how an nbyn matrix multiplied with a nby1 matrix is. It is like dot product on a larger scale with one vector dotted with a set of vectors.

So the question is about multidimentional matrix multiplication.

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# Interpretation of matrix multiplication?

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