Calculate the determinant of a matrix using Python NumPy

by | Oct 3, 2023 | Featured, Linear Algebra

Determinant

What are determinants?

The determinant of a square matrix is a scalar value that is obtained from the elements of the matrix. A determinant is defined only for a square matrix. And every square matrix has a unique determinant.

For example, let A be the following 2×2 square matrix. The determinant of A, denoted by det(A), is defined as follows:

A=\begin{bmatrix} a & b \\ c & d \end{bmatrix} \\ det(A)=(ad-bc)

If B is a 3×3 matrix, the determinant of B will be as follows:

B=\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \\ det(B)=a \times \begin{vmatrix} e & f \\ h & i \end{vmatrix} -b \times \begin{vmatrix} d & f \\ g & i \end{vmatrix} +c \times \begin{vmatrix} d & e \\ g & h \end{vmatrix} \\ =a \times (ei-fh)-b \times (di-fg)+c \times (dh-eg) \\ =aei-afh-bdi+bfg+cdh-ceg

In other words, we take the ith element of the first row of the matrix. Then, we multiply the ith element with the minor or determinant that contains all elements excepting the elements from the first row and the ith column. Please also note the alternating positive and negative signs while adding the results.

If any two rows or two columns of a square matrix are identical, then the determinant of the matrix will be 0. As a result, the matrix will not have any inverse and the square matrix will be a singular matrix.

How to calculate the determinant of a matrix using Python NumPy?

We can use the following Python code to calculate the determinant of a matrix using NumPy…

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Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

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