I have some generic matrices where I know the dimensions of the matrices, but not the actual values. I'm wanting Mathematica to use matrix identities to find a more amenable form for a proof. I define the matrices here generically because I don't know how else to tell Mathematica it's a matrix, even though I don't want to do manipulation by elements.
(X = Array[Sort[x[##]] &, {3, 1}]) // MatrixForm
$\left( \begin{array}{c} x(1,1) \\ x(1,2) \\ x(1,3) \\ \end{array} \right)$
(\mu = Array[Sort[mu[##]] &, {3, 1}]) // MatrixForm
$\left( \begin{array}{c} \mu (1,1) \\ \mu (1,2) \\ \mu (1,3) \\ \end{array} \right)$
(\CapitalSigma = Array[Sort[\Sigma[##]] &, {3, 3}]) // MatrixForm
$\left( \begin{array}{ccc} \sigma (1,1) & \sigma (1,2) & \sigma (1,3) \\ \sigma (1,2) & \sigma (2,2) & \sigma (2,3) \\ \sigma (1,3) & \sigma (2,3) & \sigma (3,3) \\ \end{array} \right)$
I apologize for potentially mixing Greek letters with Latin (because I can't put those symbols in StackExchange code apparently, but I can in Mathematica). Note that $\Sigma$ is symmetric.
I have the following expression that I want Mathematica to simplify:
$\mu_0^T \Sigma x - x^T \Sigma \mu_0$ I expect that the two terms can be combined because I saw someone else do it, but I don't know exactly how they did it.
Thread::tdlen: Objects of unequal length in {{mu[1,1],mu[1,2],mu[1,3]}} {{sig[1,1],sig[1,2],sig[1,3]},{sig[1,2],sig[2,2],sig[2,3]},{sig[1,3],sig[2,3],sig[3,3]}} x cannot be combined.
Thread::tdlen: Objects of unequal length in Transpose[x] {sig[1,1],sig[1,2],sig[1,3]} {mu[1,1]} cannot be combined.
Thread::tdlen: Objects of unequal length in Transpose[x] {sig[1,2],sig[2,2],sig[2,3]} {mu[1,2]} cannot be combined.
General::stop: Further output of Thread::tdlen will be suppressed during this calculation.
So I have several problems here. The output of this statement won't display properly (I used TeXForm to convert but it's not working here). Second, what it does display shows the elements of the matrices instead of just the matrix symbols. When I do x.mu I don't want to see the elements of the result, but want a simplification based on the whole of the matrices. And, of course, I want to get rid of the errors.
Ideas?