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Expansions of matrix-vector products 

I Expansions of the matrix-vector product AX. Consider the two matrices:





There are two important expansions of the matrix-vector product

   ole2.gif    ole3.gif

The first important expansion is:

ole4.gif   ole5.gif    ole6.gif



 where Ri is the i-th row of matrix A and the product Ri∙X is the m-dot product. This expansion follows directly from the definition of the product of two matrices.

The second important expansion is:


ole8.gif ole9.gif   

where Ci represents the i-th column of matrix A.

It can be seen that this second expansion gives the same result as the first:


Expansion (2) can be used to rewrite expressions of the type


It says they can be written in the condensed matrix form

          ole12.gif ole13.gif   .

II Expansions of the vector-matrix product XA.

There are two important expansions for the vector-matrix product:

   ole14.gif   .

The first expansion is:


 where Ci is the i-th column of matrix A and X∙Ci is the m-dot product. This expansion follows directly from the definition of the product of two matrices.

The second expansion is:




  where Ri represents the i-th row of matrix A.                                   

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