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matrix outer_product numpy

20150727

The dot product of two matrices (Eg. a matrix and it's tranpose), equals the sum of the outer products of the row-vectors & column-vectors.

a=np.matrix( "1 2; 3 4; 5 6" )

matrix([[1, 2],
        [3, 4],
        [5, 6]])

Dot product of A and A^T :

np.dot( a, a.T) 

matrix([[ 5, 11, 17],
        [11, 25, 39],
        [17, 39, 61]])

Or as the sum of the outer products of the vectors:

np.outer(a[:,0],a.T[0,:]) 

array([[ 1,  3,  5],
       [ 3,  9, 15],
       [ 5, 15, 25]])

np.outer(a[:,1],a.T[1,:])

array([[ 4,  8, 12],
       [ 8, 16, 24],
       [12, 24, 36]])

.. added up..

np.outer(a[:,0],a.T[0,:]) + np.outer(a[:,1],a.T[1,:]) 

array([[ 5, 11, 17],
       [11, 25, 39],
       [17, 39, 61]])

.. and yes it is the same as the dot product!

Note: for above, because we are forming the dot product of a matrix with its transpose, we can also write it as (not using the transpose) :

np.outer(a[:,0],a[:,0]) + np.outer(a[:,1],a[:,1])

Notes by Willem Moors. Generated on momo:/home/willem/sync/20151223_datamungingninja/pythonbook at 2019-07-31 19:22