Python Determinant

1. Use numpy.linalg.det() to Calculate the Determinant of Matrix in Python
2. Use the symPy Library to Calculate the Determinant of Matrix in Python

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