Why sum of two simple matrix is not in correct way?

Question

     clear[a];
    a = List[{0, 1, 2}, {1, 2, 3}, {2, 3, 4}]
    a // MatrixForm;
M2 = Transpose[a] // MatrixForm;
a + M2

I am trying to run this code for summation of two matrix. But finding difficulty to get simple output. In mathmatica it is in longer way and taking the whole matrix.

try (M2 = Transpose[a]) // MatrixForm; because MatrixForm is wrapper which gets in the way of further computations. — Nasser, Oct 17 '19 at 07:54
Possible duplicate of What are the most common pitfalls awaiting new users? — march, Oct 17 '19 at 15:54

score 1 · Accepted Answer · answered Oct 17 '19 at 08:35

Firstly let's try to understand what is MatrixForm.

There are a lot of "forms" that you can represent your data, as the documentation states: print with the elements arranged in a specific form. To get those: ?*Form. Now, XXXForm prints your data in a specific form, thus, it is not making an object itself. In Mathematica there is nothing like matrix, there are lists, and if your list is an array then it is a matrix, if it is rectangular array, then it is a rectangular matrix, so force, so on.

All that said, your code should be:

ClearAll[l];
l = {{0, 1, 2}, {1, 2, 3}, {2, 3, 4}};
lT = Transpose[l];
l + lT

You should try to "automize" your code as much as possible, for this particular case you can use functions:

ClearAll[matrixSum];
matrixSum[m1_, m2_] := Sum[m1, m2]

Since there are restrictions on matrics summation, you can preserve the validation:

ClearAll[matrixSum]
matrixSum[m1_ /; ArrayQ[m1, 2, Internal`RealValuedNumericQ], m2_/; ArrayQ[m2, 2, Internal`RealValuedNumericQ]] := m1 + m2 /;Dimensions[m1] === Dimensions[m2]

To make this even more accurate:

ClearAll[matrixSum];

mutrixSum::argx = "`1` and `2` matrices cannot be summed.";
mutrixSum::argx1 = "Two matrices are requred to be summed";
mutrixSum::argx2 = "No matrices given to be be summed.";
mutrixSum::argx3 = "Only two matrices are allowed as input.";

matrixSum[m1_ /; ArrayQ[m1, 2, Internal`RealValuedNumericQ], m2_/; ArrayQ[m2, 2, Internal`RealValuedNumericQ]] := m1 + m2 /;Dimensions[m1] === Dimensions[m2]

(* Overloads for failures *)
matrixSum[m1_, m2_]:= (Message[mutrixSum::argx,m1, m2]; Return[$Failed])
matrixSum[m1_]:= (Message[mutrixSum::argx1,m1]; Return[$Failed])
matrixSum[]:= (Message[mutrixSum::argx2]; Return[$Failed])
matrixSum[___]:= (Message[mutrixSum::argx3]; Return[$Failed])

You can also preserve the case for multiple matrix summations:

ClearAll[mutrixSum];

mutrixSum::argx = "All input matrices have to have the same dimensions and be rectangular.";
mutrixSum::argx1 = "At least two matrices are required to be summed";

mutrixSum[args__] := mutrixSum[List[args]]
mutrixSum[args_List?ListQ] := Plus @@ args /; AllTrue[Append[ArrayQ[#, 2, Internal`RealValuedNumericQ] & /@ args, SameQ @@ Dimensions /@ args], TrueQ]

(* Overloads for failures *)
mutrixSum[args_List?ListQ] := (Message[mutrixSum::argx]; Return[$Failed])
mutrixSum[arg_] := (Message[mutrixSum::argx1]; Return[$Failed])
mutrixSum[] := (Message[mutrixSum::argx1]; Return[$Failed])

Why sum of two simple matrix is not in correct way?

1 Answers1