title: Symbolic Matrices in Mathematica with unknown dimensions
body: <p>Is there a way to do symbolic matrix algebra in Mathematica for matrices where the dimensions are unknown? For example, if I have an MxL matrix A and an LxN matrix B, I would like to be able to enter</p>
  
  <pre><code>A.B
  </code></pre>
  
  <p>And have it give me a matrix whose element <code>ab[i,j]</code> is given by</p>
  
  <pre><code>Sum[a[i,l]*b[l,j],{l,1,L}]
  </code></pre>
  
  <p>The problem I'm working on is like this one, but involves the product of 12 matrices, including the same matrix (and its transpose) repeated several times. It will probably be possible to simplify the values of the resulting matrix, but it's not obvious whether this is possible until after I do the algebra. This may be a problem that I have to solve by hand, but it would be much easier if Mathematica could provide some help in simplifying the algebra.</p>