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: [mg104428] Re: Multiply 2 matrices where one contains differential operators with one that contains functions of x and y
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Sat, 31 Oct 2009 01:52:53 -0500 (EST)
• Reply-to: "Nasser M. Abbasi" <nma at 12000.org>

```ref (me)

>This is my solution:
>
>
> A = {{D[#1, x] & , 0 & }, {0 & , D[#1, y] & },  {D[#1, y] & , D[#1, x]
> & }}
> B = {{x*y, x^3*y, 3*x + y^2}, {2*x, x^4*y, y^2}}
>
> {rowsA, colsA} = Dimensions[A];
> {rowsB, colsB} = Dimensions[B];
>
> r = Table[0, {rowsA}, {colsB}]; (*where the result of A.B goes *)
>
> For[i = 1, i <= rowsA, i++,
>   For[j = 1, j <= colsB, j++,
>       For[ii = 1, ii <= rowsB, ii++,
>              r[[i,j]] = r[[i,j]] + A[[i,ii]] /@ {B[[ii,j]]}
>             ]
>       ]
> ]
>
> MatrixForm[r]
>

ps.After I posted the above, I noticed an extra {} inside all the matrix
elements in the result, this below is a version of the above which removes
these {}.  Those got in due to the use of the line

r[[i,j]] = r[[i,j]] + A[[i,ii]] /@ {B[[ii,j]]}

where I had to use {} around B above, else Mathematica will complain but
this caused each entry inside to have those extra {}.

So below I remove them back when done with this line.

A = {{D[#1, x] & , 0 & }, {0 & , D[#1, y] & }, {D[#1, y] & , D[#1, x] & }}
B = {{x*y, x^3*y, 3*x + y^2}, {2*x, x^4*y, y^2}}

{rowsA, colsA} = Dimensions[A];
{rowsB, colsB} = Dimensions[B];

r = Table[0, {rowsA}, {colsB}];

For[i = 1, i <= rowsA, i++,
For[j = 1, j <= colsB, j++,
{
For[ii = 1, ii <= rowsB, ii++,
r[[i, j]] = r[[i, j]] + A[[i, ii]] /@ {B[[ii, j]]}
];
r[[i, j]] = First[r[[i, j]]];
}
]
]

MatrixForm[r]

--Nasser

```

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