Following the video from MIT's OCW, the Prof. brings up many different methods, like $row * matrix$, $column * matrix$, etc. Yet don't these all come down to dot product. For example $row * matrix$ would be done using dot product, right? Is the Prof just showing all of these things to show the big picture, or what?

A little bonus: The Prof says that with the multiplication of the matrices A and B (AB) equaling to C, that the rows of C are a combination of the rows of A. Here, the columns of B must be multiplied by the matrix A (column * matrix method) to get one column of C. So, to do this you would end up doing the columns of B times all the rows of A (using dot product, right, question above), yet he says that the columns of C are a combination of the columns of A, is this just because when doing all of the rows, the columns will technically be included?

Thanks for all the help!

  • 2
    $\begingroup$ The definition of matrix multiplication comes down to dot product $\endgroup$
    – Wojowu
    Jul 11 '19 at 15:35
  • $\begingroup$ Alright, thanks, so just to clarify everything else is showing different ways you can use it? Also, could you maybe look at the bonus? Thanks for the extremely quick help! $\endgroup$ Jul 11 '19 at 15:39
  • 2
    $\begingroup$ Yes, Dr. Strang is just showing different ways of thinking about it. $\endgroup$
    – saulspatz
    Jul 11 '19 at 15:50
  • $\begingroup$ @saulspatz Alright, thanks a million, you just cleared so much up! $\endgroup$ Jul 11 '19 at 15:54
  • $\begingroup$ @saulspatz Prof. Strang is the best, isn't he! $\endgroup$ Jul 11 '19 at 15:54

Whatever the method, the final result is uniquely defined. So you can say that it amounts to dot products.

For practical reasons, the order of the operations can make a difference in convenience or speed when you multiply on paper or with a computer. When there is numerical truncation, even the values can differ.

  • $\begingroup$ Alright, thanks! Could you please take a look at the bonus? $\endgroup$ Jul 11 '19 at 15:48

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