Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

matrix times table

Is the following matrix multiplication true?

I just thought this up so I hope it's true!

---

igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: matrix times table

hi John,

Yes.  What an original idea. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: matrix times table

Thanks.  I was pretty sure it was right because I
discovered if you take the right matrix of a pair
being multiplied, and bring it up an inch so the
corners of the two matrices touch, then you can
draw a square of nxn if A=mxn and B=nxp and
then A goes down the left side of the times table
and B goes across the top of the times table.
I think this deserves a picture sometime.

n x n
square ||
goes  ||      B matrix goes up here
here   ||
--------
 
  A
matrix
goes                 times table goes here
down
here

Last edited by John E. Franklin (2014-02-25 06:39:51)

---

igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: matrix times table

Here's how I imagine
matrix A times matrix B
geometrically.
See pic.

1 x 9 + 2 x 10 = 29.

And another one is the 149 in the middle-ish.

5 x 13 + 6 x 14 = 149

See how if you take two matrices to be multiplied
and move them diagonally touching like the
diagram, you get two things.

1.) If its not a square in the north-west corner,
you can't multiply them, so the number of
columns of A has to equal the number of
rows of B.

2.) Now you can fill in any entry in the answer
just by choosing the entry spot and looking to
the left and straight up to get your numbers
to do the SOP (sum of products).

Last edited by John E. Franklin (2014-02-26 00:59:40)

---

igloo myrtilles fourmis