NumPy – Linear Algebra:

Performing Linear Algebra on several matrices which are stacked as an array.

Below are the some of Linear Algebra functions we are going work on.

dot: This will return the dot product of two arrays.

Example:

>>> import numpy as np

>>> np.dot(5,4)
20

>>> a=[[1,2],[3,4]]

>>> b=[[1,1],[1,1]]

>>> np.dot(a,b)
array([[3, 3],
[7, 7]])

vdot: This will return the dot product of two vectors.

Example:

>>> import numpy as np

>>> np.dot(5,4)
20

>>> a=[[1,2],[3,4]]

>>> b=[[1,1],[1,1]]

>>> np.vdot(a,b)
10

This is how it works in the above example ==> 1*1+2*1+3*1+4*1

inner: This will return the inner product of two arrays.

Example:

>>> import numpy as np

>>> a=[[1,2,3],[0,1,1]]

>>> b=[[1,2,3],[0,0,1]]

>>> np.inner(a,b)
array([[14, 3],
[ 5, 1]])

outer: This will return the outer product of two vectors.

Example:

>>> import numpy as np

>>> a=[[1,2],[3,4]]

>>> b=[[1,1],[1,1]]

>>> np.outer(a,b)
array([[1, 1, 1, 1],
[2, 2, 2, 2],
[3, 3, 3, 3],
[4, 4, 4, 4]])

matmul: This will return the matrix product two arrays.

Example 1:

>>> import numpy as np

>>> a=[[1,2],[3,4]]

>>> b=[[1,1],[1,1]]

>>> np.matmul(a,b)
array([[3, 3],
[7, 7]])

Example 2:

>>> import numpy as np

>>> a=[[1,2],[3,4]]

>>> b=[1,1]

>>> np.matmul(a,b)
array([3, 7])

>>> np.matmul(b,a)
array([4, 6])

tensordot: This will return the computed tensor dot product along specific aces for arrays>=1-D.

Example:

>>> import numpy as np

>>> a=np.random.randint(2, size=(1,2,3))

>>> b=np.random.randint(2, size=(3,2,1))

>>> np.tensordot(a,b,axes=((1),(1))).shape
(1, 3, 3, 1)

How it works:

we have choosen 1, 1 axes

In a ==> (1,2,3), b===> (3,2,1)===> ignore 2 now ===> (1,3,3,1)