Matrix Multiplication...
- To: mathgroup at smc.vnet.net
- Subject: [mg23551] Matrix Multiplication...
- From: "J.R. Chaffer" <jrchaff at nwlink.com>
- Date: Sat, 20 May 2000 03:10:27 -0400 (EDT)
- Organization: Northwest Link
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
New to Mathematica, and to exotic matrix techniques.
Apparently Mathematica does "ordinary" matrix multiplication
via the "dot" product symbol, "."; but when one uses the
asterisk, one gets "squaring" of two matrices:
If m1 = {{a,b},{c,d}}; and m2={{e,f},{g,h}}; then
m1*m2 = {{ae, bf},{cg,dh}}, and
m1*m1 = {{a^2, b^2},{c^2, d^2}};
while m1.m2 gives normal matrix multiplication.
What is going on here? What kind of matrix multiplication is
this "*" giving? Why does it match up with the casual appearance
of 'squaring' if m1 = m2? I tried the Mathematica function
"Outer", i.e. "Outer[Times,m1,m2]", and this is NOT the same
as the result with "*". I don't understand outer products anyway,
but apparently that is not this, whatever it is.
Can someone give me a short explanation?
Thanks.
John Chaffer
old-timer-new-person