### Related

##### kronecker_product-matrix-product

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

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

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

Calculate

##### kronecker_product-matrix-product

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

Y: matrix([M11,M12,M1...

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

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

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

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

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

Calculate

##### 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-permanent-product

m:matrix([a,b],[c,d]);

p:permanent(m);

k:kronecker_product(m...

Calculate

##### kronecker_product-matrix-product

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

kronecker_product(a,a);

Calculate

##### kronecker_product-matrix-permanent-product

a: matrix([1,2],[-1,1]);

b: permanent(a);

c: kronecker_product(...

Calculate

##### kronecker_product-matrix-product-sqrt

a:matrix([i/sqrt(2)],...

b:matrix([-i/sqrt(2)]...

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
```m:matrix([a,b],[c,d]);
[ a  b ]
(%o1)                              [      ]
[ c  d ]
(%i2) p:permanent(m);
(%o2)/R/                           a d + b c
(%i3) k:kronecker_product(m,m);
[  2              2  ]
[ a    a b  a b  b   ]
[                    ]
[ a c  a d  b c  b d ]
(%o3)                       [                    ]
[ a c  b c  a d  b d ]
[                    ]
[  2              2  ]
[ c    c d  c d  d   ]
(%i4) pp:permanent(k);
4  4      3      3       2  2  2  2        3  3      4  4
(%o4)/R/  a  d  + 4 a  b c d  + 14 a  b  c  d  + 4 a b  c  d + b  c
(%i5) q:kronecker_product(k,m);
[   3    2      2        2    2        2      2     3  ]
[  a    a  b   a  b   a b    a  b   a b    a b     b   ]
[                                                      ]
[  2     2                                  2      2   ]
[ a  c  a  d   a b c  a b d  a b c  a b d  b  c   b  d ]
[                                                      ]
[  2            2                    2             2   ]
[ a  c  a b c  a  d   a b d  a b c  b  c   a b d  b  d ]
[                                                      ]
[    2                   2      2                    2 ]
[ a c   a c d  a c d  a d    b c    b c d  b c d  b d  ]
(%o5)      [                                                      ]
[  2                   2      2                    2   ]
[ a  c  a b c  a b c  b  c   a  d   a b d  a b d  b  d ]
[                                                      ]
[    2            2                    2             2 ]
[ a c   a c d  b c    b c d  a c d  a d    b c d  b d  ]
[                                                      ]
[    2     2                                  2      2 ]
[ a c   b c    a c d  b c d  a c d  b c d  a d    b d  ]
[                                                      ]
[   3    2      2        2    2        2      2     3  ]
[  c    c  d   c  d   c d    c  d   c d    c d     d   ]
(%i6) r:permanent(q);
12  12       11      11        10  2  2  10        9  3  3  9
(%o6)/R/ a   d   + 12 a   b c d   + 114 a   b  c  d   + 876 a  b  c  d
8  4  4  8         7  5  5  7          6  6  6  6         5  7  7  5
+ 3855 a  b  c  d  + 9096 a  b  c  d  + 12412 a  b  c  d  + 9096 a  b  c  d
4  8  8  4        3  9  9  3        2  10  10  2         11  11
+ 3855 a  b  c  d  + 876 a  b  c  d  + 114 a  b   c   d  + 12 a b   c   d
12  12
+ b   c
(%i7) ```

### Related Help

Help for Kronecker_product