       Re: Multiply 2 matrices where one contains differential operators with one that contains functions of x and y

• To: mathgroup at smc.vnet.net
• Subject: [mg104452] Re: Multiply 2 matrices where one contains differential operators with one that contains functions of x and y
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Sun, 1 Nov 2009 03:58:02 -0500 (EST)

```On 10/31/09 at 1:50 AM, nma at 12000.org (Nasser M. Abbasi) wrote:

>Lets say A is a 3 by 2 matrix, which contains differential operators
>in some entries and 0 in all other entries, as in

>A= {  {  d/dx ,  0  } ,  {0  ,  d/dy } ,  {  d/dy ,  d/dx }  }

>And I want to multiply the above with say a 2 by 3 matrix whose
>entries are functions of x and y as in

>B = {{x*y,  x^3*y,  3*x + y^2}, {2*x,  x^4*y,  y^2}}

>I'd like to somehow be able to do A.B, but ofcourse here I can't, as
>I need to "apply" the operator on each function as the matrix
>multiplication is being carried out.

>I tried to somehow integrate applying the operators in A into the
>matrix multiplication of A by B, but could not find a short
>"functional" way.

Here is a short functional solution

In:= Inner[#1[#2] &, A, B]

Out= {{y, 3 x^2 y, 3}, {0, x^4, 2 y}, {x + 2, 4 y x^3 + x^3,
2 y}}

```

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