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Determinant of a Transpose Matrix | Linear Algebra using Python

Linear Algebra using Python | Determinant of a Transpose Matrix: Here, we are going to learn about the determinant of a transpose matrix and its implementation in Python.
Submitted by Anuj Singh, on June 13, 2020

Prerequisite:

• Defining Matrix using Numpy
• Determinant of a Matrix
• Transpose Matrix

Here, we will learn that the determinant of the transpose is equal to the matrix itself. This is one of the key properties in Linear Algebra and is being used in major parts of Matrix and Determinants.

Example:

Python code to find the determinant of a transpose matrix

# Linear Algebra Learning Sequence
# Transpose Determinant

import numpy as np

M1 = np.array([[2,1,4], [2,1,2], [2,3,2]])

print("Matrix (M1) :\n", M1)
print("Transpose (M1.T) :\n", M1.T)
print()

print('\n\nDeterminant of Matrix : ', np.linalg.det(M1))
print('\nDeterminant of transpose : ', np.linalg.det(M1.T))

Output:

Matrix (M1) :
 [[2 1 4]
 [2 1 2]
 [2 3 2]]
Transpose (M1.T) :
 [[2 2 2]
 [1 1 3]
 [4 2 2]]



Determinant of Matrix :  7.999999999999998

Determinant of transpose :  7.999999999999998