From: pcdhSpamMeSenseless@electrooptical.net   
      
   On 7/15/2015 4:22 PM, Michael Koch wrote:   
   > Am Mittwoch, 15. Juli 2015 22:05:45 UTC+2 schrieb Phil Hobbs:   
   >> On 07/15/2015 03:59 PM, Michael Koch wrote:   
   >>> Phil,   
   >>>   
   >>> thanks for your answer. Points 1 and 3 are clear. Point 2 is   
   >>> difficult to understand for me. I have an input which is described by   
   >>> a 2x2 matrix, then I make any operation which is also described by a   
   >>> 2x2 matrix, and the output is also a 2x2 matrix. I would understand   
   >>> it if input and output were vectors. Can a matrix be multiplied by a   
   >>> matrix? I really need an example to see how this works. Any idea   
   >>> where to find one?   
   >>>   
   >>> Michael   
   >>>   
   >>   
   >> Yes, you can multiply any MxP matrix by any PxN matrix, with an MxN   
   >> result.  You do it just as though the RH matrix were a row of column   
   >> vectors next to each other.   
   >>   
   >> A*B = C   
   >   
   > In which order must I multiply the matrices? Which is the input, A or B?   
   >   
   You have to do it from both sides,   
   For instance, to rotate a matrix, you form   
      
   M' = R^-1 M R,   
      
   where R is the rotation matrix.   
      
   You can show this by noting that a quadratic form is a scalar, i.e. it's   
   independent of coordinates.   
      
   So for any vectors V1 and V1, the rotation goes   
      
   V1^T * M * V2  	= (V1prime^T R^T) M (R V2prime)   
   		= V1prime^T (R^T M R) V2prime   
      
   For more general transformations, it's T^-1 M T .   
      
   Cheers   
      
   Phil Hobbs   
      
   --   
   Dr Philip C D Hobbs   
   Principal Consultant   
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