You don't have to define X at all; you do have to say
what you want from transpose(X).X
Maxima does know about "non-commutative multiplicative inverse"
so that X . X^^(-1) is changed to 1.
If you make a list of the simplifications or other operations
you expect to work, it might be possible to do them via tellsimp,
or rules.
There are papers on non-explicit symbolic matrix operations, but
they probably won't do what you want without some help from you.
Gray Calhoun wrote:
>Hi,
>
> I'm working with terms like "transpose(X) . X" where X is an
>unspecified n-by-p matrix. How can I define a matrix X without
>specifying the terms x_ij? I invert X'X and take derivatives of terms
>like X . b with respect to b (b is a p-by-1 vector), and would like to
>keep everything in matrix notation. I didn't find this in the
>documentation; is there another resource that I should look at?
>
>I'm using xMaxima 5.9.2 on windows XP.
>
>--
>Gray Calhoun
>
>Economics Department
>UC San Diego
>
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>