`numpy.linalg:matmul`

Signature

def matmul ( x1 , x2 , / )

Computes the matrix product.

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

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

: 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.

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)

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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)
np.linalg.matmul(b, a)

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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

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np.linalg.matmul(a, b)[0, 1, 1]
sum(a[0, 1, :] * b[0 , :, 1])

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

np.linalg.matmul([2j, 3j], [2j, 3j])

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Scalar multiplication raises an error.

np.linalg.matmul([1,2], 3)

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