Error, (in rtable/Product) use *~ for elementwise multiplication of Vectors or Matrices; use . (dot) for Vector/Matrix multiplication
An expression involving the multiplication of Vectors and/or Matrices (possibly and/or Arrays) has been constructed using the standard multiplication operator, `*`, which is ambiguous.
Note that in 2-D math `*` displays as a center dot: `⋅`, and typing a dot (using the period key) displays as `·`, as show in the following table.
When you type
It displays as
This display can be modified through the interactive Typesetting Rule Assistant.
For Vector/Matrix multiplication, use . (dot). If instead you want to perform elementwise multiplication, use *~.
This error results if Matrices, or a Matrix and a Vector, are multiplied using a commutative multiplication operator, `*`:
A ≔ a__11a__12a__21a__22
v ≔ v__1v__2
To multiply Matrices and/or Vectors together using the standard Linear Algebra multiplication operation, use the non-commutative multiplication operator, `.` (dot):
Implicit multiplication (using a space to mean multiplication) can also be ambiguous.
W ≔ Array1..2,1..2,a,b,c,d;
To multiply Vectors and/or Matrices and/or Arrays together using elementwise multiplication, use the standard multiplication operator, `*` followed by the "elementwise" operator, `~`:
A ⋅~ A
A ⋅~ W
Note that when multiplying Arrays together (not with Vectors or Matrices), the standard multiplication operator will result in the elementwise product, so the `~` is not necessary:
W ⋅ W
Note also that implicit multiplication is interpreted based on the operands, and when it can, Maple parses these as follows: For Vector/Matrix operands this will be interpreted as the `.` (dot) non-commutative multiplication operator, while for Array operands this will be interpreted as the elementwise operator:
However, best practice is to insert the explicit multiplication operator into your expressions.
Download Help Document