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Re: Abstract Symbolic Matrix operations in Mathematica


as far as I know, mma considers a matrix as a bunch of elements. Those 

may be symbolic, but not the matrix itself. This leaves two avenues to 

proceed. You may either setup a matrix with explicit dimensions and 

symbolic elements (using e.g. Array). Or you may define a new data type, 

where you have to specify the rules yourself. E.g, assuming we call a 

symbolic matrix with name x: SymMat[x]. The rules:


Transpose[a_SymMat. b_SymMat] := Transpose[b].Transpose[a]

Transpose[a_SymMat + b_SymMat] := Transpose[a] + Transpose[b]


Here I changed the definition of Transpose for simplicity. However, if 

you are not sure what you are doing, it would be better to define a new 

operator (e.g. myTranspose).

Then,f you the say:


you will get:


hope this helps, Daniel

dvshin wrote:

> Can anybody tell me how to do operations on matrix equations without computing on the element level in Mathematica? In other words, for example, if I have two "abstract" matrices A and B, what should I type to verify the following:


> (AT)^T = B^T A^T


> Would appreciate any thoughts.


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