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