# (Python Example for Beginners)

Write a NumPy program to evaluate Einstein’s summation convention of two given multidimensional arrays.

Note: In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.

Sample Solution :

Python Code :

``````
import numpy as np

a = np.array([1,2,3])
b = np.array([0,1,0])

print("Original 1-d arrays:")
print(a)
print(b)

result =  np.einsum("n,n", a, b)
print("Einstein’s summation convention of the said arrays:")
print(result)

x = np.arange(9).reshape(3, 3)
y = np.arange(3, 12).reshape(3, 3)
print("Original Higher dimension:")
print(x)
print(y)

result = np.einsum("mk,kn", x, y)
print("Einstein’s summation convention of the said arrays:")
print(result)
``````

Sample Output:

```Original 1-d arrays:
[1 2 3]
[0 1 0]
Einstein’s summation convention of the said arrays:
2
Original Higher dimension:
[[0 1 2]
[3 4 5]
[6 7 8]]
[[ 3  4  5]
[ 6  7  8]
[ 9 10 11]]
Einstein’s summation convention of the said arrays:
[[ 24  27  30]
[ 78  90 102]
[132 153 174]]```

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