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Matrix Multiplication...


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



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