# python – numpy matrix vector multiplication

## Simplest solution

Use `numpy.dot` or `a.dot(b)`. See the documentation here.

``````>>> a = np.array([[ 5, 1 ,3],
[ 1, 1 ,1],
[ 1, 2 ,1]])
>>> b = np.array([1, 2, 3])
>>> print a.dot(b)
array([16, 6, 8])
``````

This occurs because numpy arrays are not matrices, and the standard operations `*, +, -, /` work element-wise on arrays.

Note that while you can use `numpy.matrix` (as of early 2021) where `*` will be treated like standard matrix multiplication, `numpy.matrix` is deprecated and may be removed in future releases.. See the note in its documentation (reproduced below):

It is no longer recommended to use this class, even for linear algebra. Instead use regular arrays. The class may be removed in the future.

Thanks @HopeKing.

## Other Solutions

Also know there are other options:

• As noted below, if using python3.5+ the `@` operator works as youd expect:

``````>>> print(a @ b)
array([16, 6, 8])
``````
• If you want overkill, you can use `numpy.einsum`. The documentation will give you a flavor for how it works, but honestly, I didnt fully understand how to use it until reading this answer and just playing around with it on my own.

``````>>> np.einsum(ji,i->j, a, b)
array([16, 6, 8])
``````
• As of mid 2016 (numpy 1.10.1), you can try the experimental `numpy.matmul`, which works like `numpy.dot` with two major exceptions: no scalar multiplication but it works with stacks of matrices.

``````>>> np.matmul(a, b)
array([16, 6, 8])
``````
• `numpy.inner` functions the same way as `numpy.dot` for matrix-vector multiplication but behaves differently for matrix-matrix and tensor multiplication (see Wikipedia regarding the differences between the inner product and dot product in general or see this SO answer regarding numpys implementations).

``````>>> np.inner(a, b)
array([16, 6, 8])

# Beware using for matrix-matrix multiplication though!
>>> b = a.T
>>> np.dot(a, b)
array([[35,  9, 10],
[ 9,  3,  4],
[10,  4,  6]])
>>> np.inner(a, b)
array([[29, 12, 19],
[ 7,  4,  5],
[ 8,  5,  6]])
``````

## Rarer options for edge cases

• If you have tensors (arrays of dimension greater than or equal to one), you can use `numpy.tensordot` with the optional argument `axes=1`:

``````>>> np.tensordot(a, b, axes=1)
array([16,  6,  8])
``````
• Dont use `numpy.vdot` if you have a matrix of complex numbers, as the matrix will be flattened to a 1D array, then it will try to find the complex conjugate dot product between your flattened matrix and vector (which will fail due to a size mismatch `n*m` vs `n`).