Linear Algebra: What matrices are (2011)(nolaymanleftbehind.wordpress.com) |
Linear Algebra: What matrices are (2011)(nolaymanleftbehind.wordpress.com) |
You can then overlay the columns in question and simply multiply the numbers of the column entries and add them.
You also lose an intuitive property of matrix multiplication, that you can figure out where the resulting element value goes in terms of which row and which column you're iterating over. If you're iterating over the second row of the left-hand side matrix, and the third column of the right-hand-side matrix, that implies the resulting value must go in the second row, third column, of the result matrix.
Matrix multiplication can easily be visualised and taught in terms of dot products, without using additional transformations. An example: https://www.mathsisfun.com/algebra/matrix-multiplying.html
Just when you do it, you can mentally rotate it by 90degrees and line them up, this is the same thing.
Also I don’t see what’s so non-standard about a transpose, or a column reversal, but okay
Someone who is being told to multiply this entry with that entry will get confused if they don't have the high level overview. They will miss the forest for the trees.
It’s the same as with the unit circle. I teach them about pi, but also speak about Tau in case they get confused, so it makes more visual sense to them.
Same with small kids when a/b=c. I draw little arrows to show them how you can rewrite it, as purely visual trick.
Oh well, what works for one might not work for another i suppose.