Hi,
A few times ago a trainee asked me this question
"given a matrix formula, can Maple find the transpose of this formula?"
More precisely, let's say E, A, B and C are four (abstract) matrices (let's say symbols) with consistent dimensions such that E = A+B*C, can Maple "find" that ET = AT + CT * BT (where ET represents the transpose of E)?
I come back to this problem regularly because the trainee was quite frustrated by my negative answer (note she had the same request form the inverse of a matrix formula).
The best I'm capable to do is given in the attached file (transposition only).
This seems to work correctly even if did not do intensive testing.
Do you have any ideas on how to implement the transposition and inversion computation rules in Maple?
For example, given
E := A &* B^(-1))
Maple would return
Transpose(E); (B^(-1))^T &* A^T # or better E^(T) = (B^T)^(-1) &* A^T # and Inverse(E); B &* A^(-1)
Thanks in advance for you involvement