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MathGroup Archive 2003

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RE: operate a matrix of derivations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39221] RE: [mg39184] operate a matrix of derivations
  • From: F.H.Simons at tue.nl
  • Date: Tue, 4 Feb 2003 02:21:54 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

When your first matrix is a matrix of functions, then the dot product
results in a matrix of sums of products of arguments and functions. A simple
substitution then will give you the result you are looking for.

In[1]:=
mat1 = {{D[#1, x] & , 0 & }, 
   {D[#1, y] & , D[#1, x] & }}

Out[1]=
{{D[#1, x] & , 0 & }, 
  {D[#1, y] & , D[#1, x] & }}

In[2]:=
mat2 = {{x*y, x}, {x + y, 3}}

Out[2]=
{{x*y, x}, {x + y, 3}}

In[3]:=
mat1 . mat2 /. a_.*b_Function -> b[a]

Out[3]=
{{y, 1}, {1 + x, 0}}

Fred Simons
Eindhoven University of Technology

> -----Original Message-----
> From: iselig at techunix.technion.ac.il
To: mathgroup at smc.vnet.net
> [mailto:iselig at techunix.technion.ac.il]
> Sent: maandag 3 februari 2003 7:08
> To: mathgroup at smc.vnet.net
> Subject: [mg39221] [mg39184] operate a matrix of derivations
> 
> 
> I want to make a matrix of derivations, so I will be able to multiply
> it by a matrix of functions and get the result matrix
> simple example:
> 
> |d/dx   0 | |xy  x| |y   1|
> |         |.|     |=|     |
> |d/dy d/dx| |x+y 3| |x+1 0|
> 
>  thank you
> 


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