In mathematics, cross-product is simply a binary operation that is performed on two vectors in 3-dimensional space. The final generated output vector will always be perpendicular to the input vector. Vector products are also referred to as cross products. They are denoted by “**A**” x ”**B**”.

Numpy is a popular Python library that provides the “**np.cross()**” function to calculate the cross product of two vector arrays. This write-up will provide a thorough review of the Python Numpy cross-product with numerous examples. This Python guide discusses the following terms:

**What is np.cross() in Python?****Example 1: Numpy Cross Product of 2×2 Matrix****Example 2: Numpy Cross Product of 2×3 Matrix****Example 3: Numpy Cross Product of 2-D Input Array**

So let’s begin this guide!

**What is np.cross() in Python?**

To calculate the cross product of the vector arrays, the “**np.cross()**” function of the “**Numpy**” library is used in Python. The syntax of the “np.cross()” function is shown below:

```
np.cross(a, b, axisa=- 1, axisb=- 1, axisc=- 1, axis=None)
```

In the above syntax:

- The parameters “
**a**” and “**b**” indicate the first and second vector arrays respectively. - The “
**axisa**” parameter default value is the last axis or “**-1**”. This parameter defines the axis of the vector “a”. - The “
**axisb**” parameter default value is the last axis or “**-1**”. This parameter defines the axis of the vector “b”. - The “
**axisc**” parameter defines the axis of the third vector “**c**”, which contains the cross product of the given vector. - The parameter “
**axis**” represents the first, second, and third vector, including the cross product.

**Note:** The value error will be raised if the dimension of the input vector is not equal to “**2**” or “**3**”.

Let’s start with the first example of the “np.cross()” function:

**Example 1: Numpy Cross Product of 2×2 Matrix**

In the example given below, the “**np.cross()**” function of the Numpy library is used to calculate the cross product of two-dimensional vectors.

**Code:**

```
import numpy as np
val_1 = np.array([5, 4])
val_2 = np.array([5, 12])
#using np.cross()
result = np.cross(val_1, val_2)
print(result)
```

In the above code:

- The “
**numpy**” library is imported at the beginning of the program. - Two vectors having 2-dimensions are initialized inside the parentheses of the “
**np.array()**” function. - Two arrays are created using the “
**np.array()**” function and stored in a variable named “**val_1**” and “**val_2**”. - The cross product of these arrays is calculated using the “
**np.cross()**” function. The output array is calculated in the axis perpendicular to the input arrays.

**Output:**

The above snippet shows the Numpy cross product of given arrays.

**In General Maths:**

The above snippet shows the mathematical calculation of the Numpy cross product.

**Example 2: Numpy Cross Product of 2×3 Matrix(2 Rows x 3 Columns)**

In the example given below, the “**np.cross()**” calculates the cross product of the “**2×3**” matrix.

**Code:**

```
import numpy as np
val_1 = np.array([3,6,7])
val_2 = np.array([1,3,8])
# cross product of a 2X3 array
result = np.cross(val_1, val_2)
print(result)
```

In the above code:

- The “
**numpy**” library is imported at the beginning of the program. - Two vectors having 3-dimensions are initialized inside the parentheses of the “
**np.array()**” function. - The “
**np.array()**” is used to create an array, and the values of arrays are stored in a variable named “**val_1**” and “**val_2**”. - The “
**np.cross()**” takes the variable named “**val_1**” and “**val_2**” as an argument and returns the cross product.

**Note: **The 2×3 Matrix means that the input vector contains 2 rows and 3 columns or two vectors containing three elements each.

**Output**:

The above output calculates the Numpy cross-product of the given arrays.

**In General Maths:**

The mathematical calculation of the “**2×3**” matrix is shown in the above output.

**Example 3: Numpy Cross Product of 2-D Input Array**

In the example given below, the Numpy cross product of 2-D arrays is calculated using the “**np.cross()**” function.

**Code:**

```
import numpy as np
val_1 = np.array([[3,6,7],[2,2,3]])
val_2 = np.array([[2,4,8],[6,7,8]])
# cross product of a 2D-array
result = np.cross(val_1, val_2)
print(result)
```

In the above code:

- Two “
**2-D**” arrays are created with the help of a function named “**np.array()**”. - The “
**np.cross()**” calculates the cross product of the given 2-D arrays and returns the final output in 2-dimension.

**Note**: The “np.cross()” function also calculates the cross-product value of “**3-d**” arrays just like the “**2-d**” array.

**Output:**

In the above output, the Numpy cross product of 2-D arrays is calculated successfully.

That’s it from this Python Numpy guide!

**Conclusion**

To get the cross-product of the given vector arrays, the “**np.cross()**” function of the Numpy library is utilized in Python. The “**np.cross()**” function calculates the cross product of 1-dimension, 2-dimension, and 3-dimension vector arrays. The cross-product depends on the arrays being used in the program. The np.cross() function will return “1-D”, “2-D”, or “3-D” arrays depending on the input arrays.

The article provided a complete overview of the Python Numpy cross-product with multiple examples.