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import numpy as np


    

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np.__version__


    

    
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'1.11.2'

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Search results for 'linear algebra'
-----------------------------------
numpy.linalg.solve
    Solve a linear matrix equation, or system of linear scalar equations.
numpy.poly
    Find the coefficients of a polynomial with the given sequence of roots.
numpy.restoredot
    Restore `dot`, `vdot`, and `innerproduct` to the default non-BLAS
numpy.linalg.eig
    Compute the eigenvalues and right eigenvectors of a square array.
numpy.linalg.cond
    Compute the condition number of a matrix.
numpy.linalg.eigh
    Return the eigenvalues and eigenvectors of a Hermitian or symmetric matrix.
numpy.linalg.pinv
    Compute the (Moore-Penrose) pseudo-inverse of a matrix.
numpy.linalg.LinAlgError
    Generic Python-exception-derived object raised by linalg functions.

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dot(a, b, out=None)

Dot product of two arrays.

For 2-D arrays it is equivalent to matrix multiplication, and for 1-D
arrays to inner product of vectors (without complex conjugation). For
N dimensions it is a sum product over the last axis of `a` and
the second-to-last of `b`::

    dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])

Parameters
----------
a : array_like
    First argument.
b : array_like
    Second argument.
out : ndarray, optional
    Output argument. This must have the exact kind that would be returned
    if it was not used. In particular, it must have the right type, must be
    C-contiguous, and its dtype must be the dtype that would be returned
    for `dot(a,b)`. This is a performance feature. Therefore, if these
    conditions are not met, an exception is raised, instead of attempting
    to be flexible.

Returns
-------
output : ndarray
    Returns the dot product of `a` and `b`.  If `a` and `b` are both
    scalars or both 1-D arrays then a scalar is returned; otherwise
    an array is returned.
    If `out` is given, then it is returned.

Raises
------
ValueError
    If the last dimension of `a` is not the same size as
    the second-to-last dimension of `b`.

See Also
--------
vdot : Complex-conjugating dot product.
tensordot : Sum products over arbitrary axes.
einsum : Einstein summation convention.
matmul : '@' operator as method with out parameter.

Examples
--------
>>> np.dot(3, 4)
12

Neither argument is complex-conjugated:

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

For 2-D arrays it is the matrix product:

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

>>> a = np.arange(3*4*5*6).reshape((3,4,5,6))
>>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))
>>> np.dot(a, b)[2,3,2,1,2,2]
499128
>>> sum(a[2,3,2,:] * b[1,2,:,2])
499128

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