numpy.linalg.matmul

linalg.matmul(x1, x2, /)

Computes the matrix product.

This function is Array API compatible, contrary to numpy.matmul.

Parameters:

x1array_like

The first input array.

x2array_like

The second input array.

Returns:

outndarray

The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors.

Raises:

ValueError

If the last dimension of x1 is not the same size as the second-to-last dimension of x2.

If a scalar value is passed in.

See also

numpy.matmul

Examples

For 2-D arrays it is the matrix product:

>>> a = np.array([[1, 0],
...               [0, 1]])
>>> b = np.array([[4, 1],
...               [2, 2]])
>>> np.linalg.matmul(a, b)
array([[4, 1],
       [2, 2]])

For 2-D mixed with 1-D, the result is the usual.

>>> a = np.array([[1, 0],
...               [0, 1]])
>>> b = np.array([1, 2])
>>> np.linalg.matmul(a, b)
array([1, 2])
>>> np.linalg.matmul(b, a)
array([1, 2])

Broadcasting is conventional for stacks of arrays

>>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))
>>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))
>>> np.linalg.matmul(a,b).shape
(2, 2, 2)
>>> np.linalg.matmul(a, b)[0, 1, 1]
98
>>> sum(a[0, 1, :] * b[0 , :, 1])
98

Vector, vector returns the scalar inner product, but neither argument is complex-conjugated:

>>> np.linalg.matmul([2j, 3j], [2j, 3j])
(-13+0j)

Scalar multiplication raises an error.

>>> np.linalg.matmul([1,2], 3)
Traceback (most recent call last):
...
ValueError: matmul: Input operand 1 does not have enough dimensions ...