# Do all matrix multiplication methods boil down to dot product?

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!

• The definition of matrix multiplication comes down to dot product – Wojowu Jul 11 '19 at 15:35
• 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! – BeastCoder2 Jul 11 '19 at 15:39
• Yes, Dr. Strang is just showing different ways of thinking about it. – saulspatz Jul 11 '19 at 15:50
• @saulspatz Alright, thanks a million, you just cleared so much up! – BeastCoder2 Jul 11 '19 at 15:54
• @saulspatz Prof. Strang is the best, isn't he! – BeastCoder2 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.

• Alright, thanks! Could you please take a look at the bonus? – BeastCoder2 Jul 11 '19 at 15:48