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But Foo Keong,Are you seriously suggesting that Mike should use these observation about the commutativity of matrix operations and their determinants to teach his granddaughter why -x-=+?
I suspect that Mike doesn't understand it himself. Who is to educate the educator? Andy Ng Foo Keong wrote:
re: Ed Wall message to Michael about matrices.
Here's the modern math-talk about it:-
If _a_ is a 3D transformation/function/mapping represented by square matrix A,
and _b_ is a 3D transformation/function/mapping represented by square matrix B,
then the composite function _a_ @ _b_ ("_b_ followed by _a_" or the
other way round, depending on convention but stick to that convention)
is represented by the matrix AB. functions and matrices are non-commutative
in general. but since
det(AB) = det(A) det(B)
the determinant map det:A |---> det A defines a homomorphism from
square matrices to the integers. this is where you "lose"
non-commutativity. although AB is not the same as BA in general,
det(AB) = det(A) det(B) = det(B) det(A) = det(BA)
when you are back to the numbers-world from your excursion into the
Matrix world,
the commutative law operates again.
Foo Keong
NIE, Singapore
-- ------------------------------------------------------------------------ Andy Blunden http://home.mira.net/~andy/ Hegel's Logic with a Foreword by Andy Blunden: From Erythrós Press and Media <http://www.erythrospress.com/>. _______________________________________________ xmca mailing list xmca@weber.ucsd.edu http://dss.ucsd.edu/mailman/listinfo/xmca