
Re: Working with arrays
Posted:
Jun 17, 2013 6:18 AM


Am 16.06.2013 11:12, schrieb amannucci: > lA = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; > xtest = {4, 5, 6}; > lA\[CenterDot]xtest (* First case *) > {{a, b}, {c, d}} . {x, y} (* Second case *) > > The output is: > > {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}\[CenterDot]{4, 5, 6} > > {a x + b y, c x + d y}
The Dotmultiplication operator is overloaded with conventional physical applications.
In the mathematical sense you may declare matrix multiplication from the left with row vectors
{1,2,3}.{{1,2,3},{4,5,6},{7,8,9}}
or multiplication from the right with column vectors
{{1,2,3},{4,5,6},{7,8,9}.{{1},{2},{3}}
But since the most common three bilinear procedures on higher dimensional objects of maximal tensor rank 2:
1) scalar multiplication with implicitely assumed euclidean metrics, 2) applying forms on vectors and tensors of rank 2 3) matrix multiplication procedures
are obcsured in physics textbooks, completely, Mathematica, as a user friendly package, deliberately is guessing if a given Dot product may make any sense.
A hint to the background of this strange behavour is given in the "more information" statement in the Help for Dot:
" When its arguments are not lists or sparse arrays, Dot remains unevaluated"
Evaluate[lA].Evaluate[xtest]
is working as expected.
Take it as a hint that Dot is a generic name for a library of highly specialized subfunctions, that will be called with the arguments by name and not by value or on the stack.
It is the same reason why Plot or Integrate do not Evaluate the functional arguments. If needed, the values explicitely have to be handed over with an Evaluate beforehand in order to replace the name by its value in an argument at a Hold position.
But this behaviour is not documented for Dot.
Attributes[Dot] ...
Perhaps this behaviour may force numerical linear programmers to use the correct mathematical tensor categories even in case of simple numerics with numerical arrays  or perhaps they will use other packages not so sophisticated.

Roland Franzius

