# Python Determinant

Fariba Laiq Jan 30, 2023 May 03, 2022

The `determinant` of a matrix is a scalar number that is only associated with square matrices. For a square matrix `[[1,2], [3,4]]`, the determinant is calculated as `(1x4) - (2x3)`.

## Use `numpy.linalg.det()` to Calculate the Determinant of Matrix in Python

The `NumPy` package has a module named `linalg` which stands for linear algebra. This module provides a built-in method `det()` to calculate the determinant of a matrix in Python.

To use the `NumPy` package, we must install it first using the following command.

``````#Python 3.x
pip install numpy
``````

After the installation, we can find the determinant of any square matrix using the following syntax.

Syntax:

``````#Python 3.x
numpy.linalg.det(matrix)
``````

### Determinant of a `2x2` Matrix in Python

In the following code, we have created a `2x2` NumPy array and calculated the determinant of the matrix using the `det()` method. Finally, we have rounded off the determinant because this method returns the determinant as a float data type.

Example Code:

``````#Python 3.x
import numpy as np
matrix = np.array([[7, 5], [2, 4]])
det = np.linalg.det(matrix)
print("Determinant of the matrix is:", round(det))
``````

Output:

``````#Python 3.x
Determinant of the matrix is: 18
``````

### Determinant of a `3x3` Matrix in Python

We can calculate the determinant of a `3x3` or any dimension of a square matrix using the same procedure. In the following code, we constructed a `3x3` NumPy array and used the `det()` method to determine the determinant of the matrix.

Example Code:

``````#Python 3.x
import numpy as np
matrix = np.array([[7, 5, 3], [2, 4, 1], [5, 8, 6] ])
det = np.linalg.det(matrix)
print("Determinant of the matrix is:", round(det))
``````

Output:

``````#Python 3.x
Determinant of the matrix is: 65
``````

## Use the `symPy` Library to Calculate the Determinant of Matrix in Python

The `symPy` is an open-source library in Python for symbolic computation. We can perform various algebraic and other mathematical operations using this library.

To use `symPy`, we have to install it first using the following command.

``````#Python 3.x
pip install sympy
``````

### `Determinant` of a `2x2` Matrix in Python

We have created a `2x2` matrix using the `sympy.Matrix()` method in the following code. Then we have found the determinant by calling the `det()` method with the matrix.

Example Code:

``````#Python 3.x
import sympy as sp
matrix=sp.Matrix([[7 , 5],[2 , 4]])
determinant=matrix.det()
print("Determinant of the matrix is:", determinant)
``````

Output:

``````#Python 3.x
Determinant of the matrix is: 18
``````

### `Determinant` of a `3x3` Matrix in Python

The procedure is the same for a `3x3` matrix or a square matrix of any dimension to find the determinant. In the following code, we have created a `3x3` matrix and found its determinant using the `det()` method with the matrix.

Example Code:

``````#Python 3.x
import sympy as sp
matrix=sp.Matrix([[7, 5, 3], [2, 4, 1], [5, 8, 6] ])
determinant=matrix.det()
print("Determinant of the matrix is:", determinant)
``````

Output:

``````#Python 3.x
Determinant of the matrix is: 65
``````
Author: Fariba Laiq

I am Fariba Laiq from Pakistan. An android app developer, technical content writer, and coding instructor. Writing has always been one of my passions. I love to learn, implement and convey my knowledge to others.