# numpy.kron#

numpy.kron(a, b)[source]#

Kronecker product of two arrays.

Computes the Kronecker product, a composite array made of blocks of the second array scaled by the first.

Parameters:
a, barray_like
Returns:
outndarray

`outer`

The outer product

Notes

The function assumes that the number of dimensions of a and b are the same, if necessary prepending the smallest with ones. If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`, the Kronecker product has shape `(r0*s0, r1*s1, ..., rN*SN)`. The elements are products of elements from a and b, organized explicitly by:

```kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
```

where:

```kt = it * st + jt,  t = 0,...,N
```

In the common 2-D case (N=1), the block structure can be visualized:

```[[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
[  ...                              ...   ],
[ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]
```

Examples

```>>> import numpy as np
>>> np.kron([1,10,100], [5,6,7])
array([  5,   6,   7, ..., 500, 600, 700])
>>> np.kron([5,6,7], [1,10,100])
array([  5,  50, 500, ...,   7,  70, 700])
```
```>>> np.kron(np.eye(2), np.ones((2,2)))
array([[1.,  1.,  0.,  0.],
[1.,  1.,  0.,  0.],
[0.,  0.,  1.,  1.],
[0.,  0.,  1.,  1.]])
```
```>>> a = np.arange(100).reshape((2,5,2,5))
>>> b = np.arange(24).reshape((2,3,4))
>>> c = np.kron(a,b)
>>> c.shape
(2, 10, 6, 20)
>>> I = (1,3,0,2)
>>> J = (0,2,1)
>>> J1 = (0,) + J             # extend to ndim=4
>>> S1 = (1,) + b.shape
>>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))
>>> c[K] == a[I]*b[J]
True
```