Matrix multiplication: Difference between revisions

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 =={{header|Mathematica}}==
-<lang mathematica>M1 = {{1, 2},
-      {3, 4},
-      {5, 6},
-      {7, 8}}
-M2 = {{1, 2, 3},
-      {4, 5, 6}}
-M = M1.M2</lang>
+The Wolfram Language supports both dot products and element-wise multiplication of matrices.
-Or without the variables:
+This computes a dot product:
-<lang mathematica>{{1, 2}, {3, 4}, {5, 6}, {7, 8}}.{{1, 2, 3}, {4, 5, 6}}</lang>
+<lang mathematica>Dot[{{a, b}, {c, d}}, {{w, x}, {y, z}}]</lang>
-The result is:
-<lang mathematica>{{9, 12, 15}, {19, 26, 33}, {29, 40, 51}, {39, 54, 69}}</lang>
-<lang mathematica>matrixMul[m1_, m2_] := Table[Times @@ {a, b} // Tr, {a, m1}, {b, Transpose@m2}]
-matrixMul2[m1_, m2_] :=Table[Sum[Times @@ i, {i, Transpose@{a, b}}], {a, m1}, {b, Transpose@m2}]
+This also computes a dot product, using the infix . notation:
-a = {{1, 2}, {3, 4}, {5, 6}, {7, 8}};
-b = {{1, 2, 3}, {4, 5, 6}};
+<lang mathematica>{{a, b}, {c, d}} . {{w, x}, {y, z}}</lang>
-matrixMul[a, b]
-matrixMul2[a, b]</lang>
+This does element-wise multiplication of matrices:
+<lang mathematica>Times[{{a, b}, {c, d}}, {{w, x}, {y, z}}]</lang>
+With the following infix notations '*' and ' ' (space):
+<lang mathematica>{{a, b}, {c, d}}*{{w, x}, {y, z}}</lang>
+<lang mathematica>{{a, b}, {c, d}} {{w, x}, {y, z}}</lang>
+In all cases matrices can be fully symbolic or numeric or mixed symbolic and numeric.
+Numeric matrices support arbitrary numerical magnitudes, arbitrary precision as well
+as complex numbers.
 =={{header|MATLAB}} / {{header|Octave }}==