1. Aug 28, 2012 #1

   matqkks

   

   Why is the row space of a matrix important?

    

   matqkks, Aug 28, 2012
2. 
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3. Aug 28, 2012 #2

   genericusrnme

   

   The same reason the column space is important.
   One example is basic multiplication;
   Multiplying a matrix with a vector to the right gives linear combinations of the columns, multiplying with a vector to the left gives linear combinations of the rows.

    

   genericusrnme, Aug 28, 2012
4. Aug 30, 2012 #3

   Bacle2

   

   Science Advisor

   The row space is used in the fundamental theorem of linear algebra:
   
   http://en.wikipedia.org/wiki/Fundamental_theorem_of_linear_algebra
   
   which relates row space, column space, kernel and cokernel.
   
   Together, of course, with the rank-nullity theorem.

    

   Last edited: Aug 30, 2012

   Bacle2, Aug 30, 2012

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