# NumPy: Compute the Kronecker product of two given mulitdimension arrays

## NumPy: Linear Algebra Exercise-8 with Solution

Write a NumPy program to compute the Kronecker product of two given mulitdimension arrays.

Note: In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a generalization of the outer product (which is denoted by the same symbol) from vectors to matrices, and gives the matrix of the tensor product with respect to a standard choice of basis. The Kronecker product should not be confused with the usual matrix multiplication, which is an entirely different operation.

If A is an m × n matrix and B is a p × q matrix, then the Kronecker product A ⊗ B is the mp × nq block matrix:

**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.kron(a, b)
print("Kronecker product 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.kron(x, y)
print("Kronecker product of the said arrays:")
print(result)
```

Sample Output:

Original 1-d arrays: [1 2 3] [0 1 0] Kronecker product of the said arrays: [0 1 0 0 2 0 0 3 0] Original Higher dimension: [[0 1 2] [3 4 5] [6 7 8]] [[ 3 4 5] [ 6 7 8] [ 9 10 11]] Kronecker product of the said arrays: [[ 0 0 0 3 4 5 6 8 10] [ 0 0 0 6 7 8 12 14 16] [ 0 0 0 9 10 11 18 20 22] [ 9 12 15 12 16 20 15 20 25] [18 21 24 24 28 32 30 35 40] [27 30 33 36 40 44 45 50 55] [18 24 30 21 28 35 24 32 40] [36 42 48 42 49 56 48 56 64] [54 60 66 63 70 77 72 80 88]]

**Python Code Editor:**

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**Previous:** Write a NumPy program to compute the eigenvalues and right eigenvectors of a given square array.

**Next:** Write a NumPy program to compute the condition number of a given matrix.

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## Python: Tips of the Day

**Negative Indexing:**

In Python you can use negative indexing. While positive index starts with 0, negative index starts with -1.

name="Welcome" print(name[0]) print(name[-1]) print(name[0:3]) print(name[-1:-4:-1])

Output:

W e Wel emo

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