# numpy.linalg.outer#

linalg.outer(x1, x2, /)[source]#

Compute the outer product of two vectors.

This function is Array API compatible. Compared to `np.outer` it accepts 1-dimensional inputs only.

Parameters:
x1(M,) array_like

One-dimensional input array of size `N`. Must have a numeric data type.

x2(N,) array_like

One-dimensional input array of size `M`. Must have a numeric data type.

Returns:
out(M, N) ndarray

`out[i, j] = a[i] * b[j]`

Examples

Make a (very coarse) grid for computing a Mandelbrot set:

```>>> rl = np.linalg.outer(np.ones((5,)), np.linspace(-2, 2, 5))
>>> rl
array([[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.]])
>>> im = np.linalg.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
>>> im
array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
[0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
[0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
>>> grid = rl + im
>>> grid
array([[-2.+2.j, -1.+2.j,  0.+2.j,  1.+2.j,  2.+2.j],
[-2.+1.j, -1.+1.j,  0.+1.j,  1.+1.j,  2.+1.j],
[-2.+0.j, -1.+0.j,  0.+0.j,  1.+0.j,  2.+0.j],
[-2.-1.j, -1.-1.j,  0.-1.j,  1.-1.j,  2.-1.j],
[-2.-2.j, -1.-2.j,  0.-2.j,  1.-2.j,  2.-2.j]])
```

An example using a “vector” of letters:

```>>> x = np.array(['a', 'b', 'c'], dtype=object)
>>> np.linalg.outer(x, [1, 2, 3])
array([['a', 'aa', 'aaa'],
['b', 'bb', 'bbb'],
['c', 'cc', 'ccc']], dtype=object)
```