[Maxima] Symbolic Matrix

Paulo Grahl pgrahl at gmail.com
Fri Feb 27 13:25:26 CST 2009

```Dear list members:
I need some advice on how to implement some symbolic calculations with matrices.
For example, let's say I declare F and G as matrices. (nonscalar)
Then I am interested in, for example, simplifying tr(F.G+G.F) to
2*tr(F.G), where "tr" is declared as a linear function (matrix trace).
I would also be interested in obtaining differentials of the form
dF^^-1 = -F^^-1.dF.F^^-1 (provided the inverse exists)
or
d ln |F| = tr(F^^-1 dF)
or
d tr(F) = tr(dF)
or
declaring a symbolic identity matrix "I" and making sure F.I=F,  F^^0=I, etc.

among others.

Is there a symbolic matrix package where one could implement such rules ?
I have already looked into Richard Fateman's excellent article
"Manipulation of Matrices Symbolically", but that is much more general
that what I need. In my case all matrices are square, with same nxn
dimension, the inverses are assumed to exist, etc.

Any help is appreciated.
best
Paulo

Paulo Gustavo Grahl, CFA
------------------------------------------
pgrahl at gmail.com
pgrahl at fgvmail.br
+55(21) 8809-9254