Consider a list of matrices
(%i2) s : [matrix([1,2],[3,4]), matrix([a,b],[c,d])]$
OK
(%i3) first(s).first(s) + second(s).second(s);
(%o3) matrix([b*c+a^2+7,b*d+a*b+10],[c*d+a*c+15,d^2+b*c+22])
Can we do this with s.s? No, to get the dot product to work, we need
to set matrix_element_mult to noncummuative multiplication, but then
the matrix products are done with noncommuative multiplication too.
(%i4) matrix_element_mult : "."$
(%i5) s.s;
(%o5) matrix([b . c+a^^2+7,b . d+a . b+10],[d . c+c . a+15,d^^2+c . b+22])
When ratmx is true (often a good choice), it's worse
(%i6) ratmx : true$
(%i7) s.s;
Unsimplified:
(%o7) matrix([1,2],[3,4])^2+matrix([a,b],[c,d])^2
(%i8) expand(%,0,0);
(%o8) matrix([a^2+1,b^2+4],[c^2+9,d^2+16])
Barton
Barton