# How to get the result of a multiplication between a matrix and a vector?

Posted 6 years ago
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 I want to get the result of a multiplication between a matrix and a vector, basically I want to do a change of reference frame of a vector, so I cannot perform this operation in mathematica. A = {{2, 4}, {2, 1}} // MatrixForm C2 = {{6}, {5}} // MatrixForm A.C2 (*This does not work*) I want to get something like this: {{2, 4}, {2, 1}}.{{6}, {5}} // MatrixForm Actually I have something more complex, but this is enough to show my problem.Do you have any suggestion?
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Posted 6 years ago
 MatrixForm is a print wrapper for display purposes. Don't use it in the definitions, only to display results. Also, it is best to not begin user-defined symbols with upper case, since that can conflict with built-in names. In[1]:= a = {{2, 4}, {2, 1}}; c2 = {{6}, {5}}; a.c2 Out[3]= {{32}, {17}} 
Posted 6 years ago
 It's also important to recognize that the dot product operator is also the operator for multiplying matrices, which allows some things which are not standard linear algebra.
Posted 6 years ago
 Frank makes an important point. In Mathematica the dot operator is overloaded, and can be matrix multiplication, matrix-vector multiplication,vector-matrix multiplication, or the scalar dot product of vectors, depending on context. If possible, Mathematica also conforms the vectors as needed. For example, a nxm matrix can multiply a m-wide row vector without objection.
Posted 6 years ago
 More simply In[20]:= {{2, 4}, {2, 1}}.{6, 5} Out[20]= {32, 17} 
Posted 6 years ago
Posted 6 years ago
 Thanks for your explanation. Frank Kampas
 I find it helpful to use MatrixForm as follows: (A={{2,4},{2,1}})//MatrixForm (C2={{6},{5}})//MatrixForm (A.C2 )//MatrixForm In this way, the MatrixForm is applied to the output of the Set (=) function rather than the second argument of Set.