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Related

kronecker_product-matrix-product-sqrt

X: matrix([0,1],[1,0]);

R: matrix([0,0],[0,1]);

Y: matrix([0,-sqrt(-1...

Calculate

kronecker_product-matrix-product

a: matrix([1, 0], [0,...

b: matrix([1, 1], [1,...

c: matrix([3, 7], [5,...

Calculate

kronecker_product-matrix-product

a: matrix([1, 0], [0,...

b: matrix([1, 1], [1,...

c: matrix([3, 7], [5,...

Calculate

kronecker_product-matrix-product

U: matrix([1,1,1,1],[...

I: matrix([1,0],[0,1]);

S_z: matrix([1,0],[0,...

Calculate

kronecker_product-matrix-product

a: matrix([1, 0], [0,...

b: matrix([1, 1], [1,...

c: matrix([3, 7], [5,...

Calculate

kronecker_product-matrix-product

a: matrix([1, 0], [0,...

b: matrix([1, 1], [1,...

c: matrix([3, 7], [5,...

Calculate

kronecker_product-matrix-product

a: matrix([1,2]);

b: matrix([9]);

kronecker_product(a, b);

Calculate

kronecker_product-matrix-product-sqrt

X: matrix([0,1],[1,0]);

I: matrix([1,0],[0,1]);

H: (1/sqrt(2))*matrix...

Calculate

kronecker_product-matrix-product

a: matrix([1, 0], [0,...

b: matrix([1, 1], [1,...

c: matrix([3, 7], [5,...

Calculate

kronecker_product-matrix-product

a: matrix([4,9]);

b: matrix([7,5,1,6]);

kronecker_product(a, b);

Calculate

kronecker_product

Run Example
(%i1)I: matrix([1,0],[0,1]);
                                   [ 1  0 ]
(%o1)                              [      ]
                                   [ 0  1 ]
(%i2) S_z: matrix([1,0],[0,-1]);
                                  [ 1   0  ]
(%o2)                             [        ]
                                  [ 0  - 1 ]
(%i3) S_x: matrix([0,1],[1,0]);
                                   [ 0  1 ]
(%o3)                              [      ]
                                   [ 1  0 ]
(%i4) S_y: matrix([0,-%i],[%i,0]);
                                 [ 0   - %i ]
(%o4)                            [          ]
                                 [ %i   0   ]
(%i5) [vals,vecs]:eigenvectors(kronecker_product(S_x,S_y));
(%o5) [[[- 1, 1], [2, 2]], [[[1, 0, 0, - %i], [0, 1, %i, 0]], 
                                             [[1, 0, 0, %i], [0, 1, - %i, 0]]]]
(%i6) 
Run Example
x1: matrix([0, 1, 0],[0,0,1],[1,0,0]);
                                  [ 0  1  0 ]
                                  [         ]
(%o1)                             [ 0  0  1 ]
                                  [         ]
                                  [ 1  0  0 ]
(%i2) x2: matrix([1,0,0], [0,1,0], [0,0,1]);
                                  [ 1  0  0 ]
                                  [         ]
(%o2)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i3) A:kronecker_product(x1, x2);
                         [ 0  0  0  1  0  0  0  0  0 ]
                         [                           ]
                         [ 0  0  0  0  1  0  0  0  0 ]
                         [                           ]
                         [ 0  0  0  0  0  1  0  0  0 ]
                         [                           ]
                         [ 0  0  0  0  0  0  1  0  0 ]
                         [                           ]
(%o3)                    [ 0  0  0  0  0  0  0  1  0 ]
                         [                           ]
                         [ 0  0  0  0  0  0  0  0  1 ]
                         [                           ]
                         [ 1  0  0  0  0  0  0  0  0 ]
                         [                           ]
                         [ 0  1  0  0  0  0  0  0  0 ]
                         [                           ]
                         [ 0  0  1  0  0  0  0  0  0 ]
(%i4) x3: matrix([0, 1, 0],[0,0,1],[1,0,0]);
                                  [ 0  1  0 ]
                                  [         ]
(%o4)                             [ 0  0  1 ]
                                  [         ]
                                  [ 1  0  0 ]
(%i5) x4: matrix([1,0,0], [0,1,0], [0,0,1]);
                                  [ 1  0  0 ]
                                  [         ]
(%o5)                             [ 0  1  0 ]
                                  [         ]
                                  [ 0  0  1 ]
(%i6) B:kronecker_product(x4, x3);
                         [ 0  1  0  0  0  0  0  0  0 ]
                         [                           ]
                         [ 0  0  1  0  0  0  0  0  0 ]
                         [                           ]
                         [ 1  0  0  0  0  0  0  0  0 ]
                         [                           ]
                         [ 0  0  0  0  1  0  0  0  0 ]
                         [                           ]
(%o6)                    [ 0  0  0  0  0  1  0  0  0 ]
                         [                           ]
                         [ 0  0  0  1  0  0  0  0  0 ]
                         [                           ]
                         [ 0  0  0  0  0  0  0  1  0 ]
                         [                           ]
                         [ 0  0  0  0  0  0  0  0  1 ]
                         [                           ]
                         [ 0  0  0  0  0  0  1  0  0 ]
(%i7) c:matrix_sum(A,B);
                 [ 0  0  0  1  0  0  0  0  0 ]  [ 0  1  0  0  0  0  0  0  0 ]
                 [                           ]  [                           ]
                 [ 0  0  0  0  1  0  0  0  0 ]  [ 0  0  1  0  0  0  0  0  0 ]
                 [                           ]  [                           ]
                 [ 0  0  0  0  0  1  0  0  0 ]  [ 1  0  0  0  0  0  0  0  0 ]
                 [                           ]  [                           ]
                 [ 0  0  0  0  0  0  1  0  0 ]  [ 0  0  0  0  1  0  0  0  0 ]
                 [                           ]  [                           ]
(%o7) matrix_sum([ 0  0  0  0  0  0  0  1  0 ], [ 0  0  0  0  0  1  0  0  0 ])
                 [                           ]  [                           ]
                 [ 0  0  0  0  0  0  0  0  1 ]  [ 0  0  0  1  0  0  0  0  0 ]
                 [                           ]  [                           ]
                 [ 1  0  0  0  0  0  0  0  0 ]  [ 0  0  0  0  0  0  0  1  0 ]
                 [                           ]  [                           ]
                 [ 0  1  0  0  0  0  0  0  0 ]  [ 0  0  0  0  0  0  0  0  1 ]
                 [                           ]  [                           ]
                 [ 0  0  1  0  0  0  0  0  0 ]  [ 0  0  0  0  0  0  1  0  0 ]
(%i8) rang(x2);
                                    [ 1  0  0 ]
                                    [         ]
(%o8)                          rang([ 0  1  0 ])
                                    [         ]
                                    [ 0  0  1 ]
(%i9) 
Run Example
a: matrix([1, 0], [0, 1]);
                                   [ 1  0 ]
(%o1)                              [      ]
                                   [ 0  1 ]
(%i2) b: matrix([1, 1], [1, 1], [1, 1]);
                                   [ 1  1 ]
                                   [      ]
(%o2)                              [ 1  1 ]
                                   [      ]
                                   [ 1  1 ]
(%i3) c: matrix([3, 7], [5, 11], [3, 14]);
                                   [ 3  7  ]
                                   [       ]
(%o3)                              [ 5  11 ]
                                   [       ]
                                   [ 3  14 ]
(%i4) d: matrix([6, 3], [4, 7]);
                                   [ 6  3 ]
(%o4)                              [      ]
                                   [ 4  7 ]
(%i5) e: matrix([5, 7], [11, 1]);
                                   [ 5   7 ]
(%o5)                              [       ]
                                   [ 11  1 ]
(%i6) kronecker_product(a, b);
                                [ 1  1  0  0 ]
                                [            ]
                                [ 1  1  0  0 ]
                                [            ]
                                [ 1  1  0  0 ]
(%o6)                           [            ]
                                [ 0  0  1  1 ]
                                [            ]
                                [ 0  0  1  1 ]
                                [            ]
                                [ 0  0  1  1 ]
(%i7) kronecker_product(b, a);
                                [ 1  0  1  0 ]
                                [            ]
                                [ 0  1  0  1 ]
                                [            ]
                                [ 1  0  1  0 ]
(%o7)                           [            ]
                                [ 0  1  0  1 ]
                                [            ]
                                [ 1  0  1  0 ]
                                [            ]
                                [ 0  1  0  1 ]
(%i8) 

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