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Mathematics Algebra Wolfram Language

How to obtain 3x3 matrices as output from the computation of 2x2 matrices

Nomsa Ledwaba

Posted 4 years ago

Please help me to achieve the 3 x 3 from the steps I undertook. I did line1 since ad A1 (2 x 2 matrix). I attempted to equate line 2, hoping to get line 3 (output which is 3 x 3 matrix). I attempted to equate line 2, hoping to get line 3 (output which is 3 x 3 matrix). I added the 'commented out' part of the code which I suspect it is a direction in moving from a 2x2 to 3x3 matrix, it's just that I don't have the right Mathematica syntax. See attachment. (_____ This is how one enters the input : {A1={{1,0},{0,-1}}, \ A2={{0,1},{0,0}}, A3={{0,0},{1,0}}} __________) (_____ Note that the order in which one inputs matters _______) newlistSym = Input["Please input a basis in a list form"]; dim = Length[newlistSym]; AdjointMatrixCommutator[A1, A3] = Dot[A1, A3] - Dot[A3, A1] (* adA3 = AdjointMatrixCommutator[A1,A3] == Table[c[1, 3, k], {k, 1, \ dim}]) AdjointMatrixCommutator[A1, A2] = Dot[A1, A2] - Dot[A2, A1] (ad A2 = AdjointMatrixCommutator[A1,A2] == c[1, 2, k], {k, 1, dim}) AdjointMatrixCommutator[A1, A1] = Dot[A1, A1] - Dot[A1, A1] (ad A1 = AdjointMatrixCommutator[A1,A3] == c[1, 1, k], {k, 1, dim}) Attachments:* Practice4.1.nb

Please help me to achieve the 3 x 3 from the steps I undertook. I did line1 since ad A1 (2 x 2 matrix). I attempted to equate line 2, hoping to get line 3 (output which is 3 x 3 matrix). I attempted to equate line 2, hoping to get line 3 (output which is 3 x 3 matrix). I added the 'commented out' part of the code which I suspect it is a direction in moving from a 2x2 to 3x3 matrix, it's just that I don't have the right Mathematica syntax. See attachment. matrix_computation1

(*_____ This is how one enters the input : {A1={{1,0},{0,-1}}, \
A2={{0,1},{0,0}}, A3={{0,0},{1,0}}}  __________*)

(*_____ Note that the order in which one inputs matters  _______*)
newlistSym = Input["Please input a basis in a list form"];
dim = Length[newlistSym];
AdjointMatrixCommutator[A1, A3] = Dot[A1, A3] - Dot[A3, A1]
(* adA3 = AdjointMatrixCommutator[A1,A3] == Table[c[1, 3, k], {k, 1, \
dim}]*)
AdjointMatrixCommutator[A1, A2] = Dot[A1, A2] - Dot[A2, A1]
(*ad A2 = AdjointMatrixCommutator[A1,A2] == c[1, 2, k], {k, 1, dim}*)
AdjointMatrixCommutator[A1, A1] = Dot[A1, A1] - Dot[A1, A1]
(*ad A1 = AdjointMatrixCommutator[A1,A3] == c[1, 1, k], {k, 1, dim}*)

POSTED BY: Nomsa Ledwaba

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Nomsa Ledwaba

Posted 4 years ago

Thank you for responding. The reason of doing duplication for each computation was to show that the outputs were correct, however, the outputs must be in a 3 x 3 matrix. So that means for , the output ad[A3] should be ad [A3] = {{0, 0, 0}, {0, 2, 0}, {0, 0, - 2}} ad [A2] = {{0, 0, 0}, { 0, 2, 0}, {0, 0, 0}} ad [A1] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} See updated attachment. For the rest of the code in terms of using functions you are very correct and I appreciate your helpful input. If I used a similar definition of function array adjointMatrixCommutator[x_, newlistSym _] := Module[{vars, f}, vars = Array[f, Length[newlistSym ]] in the earlier part of the code wouldn't that confuse the rest of the code or is it a subsequent computation?

POSTED BY: Nomsa Ledwaba

Ta'a Nwa Dombou

Posted 4 years ago

POSTED BY: Ta'a Nwa Dombou

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