How to create an augmented matrix using Python NumPy?

by | Oct 3, 2023 | Linear Algebra

Augmented Matrix

What is an augmented matrix?

An augmented matrix is a matrix that is obtained by appending the columns of two given matrices. Let’s say we are given two matrices A and B. A is an mxn matrix and B is a mxp matrix. Now, we can append the columns of B after the columns of A. The created matrix C will be an augmented matrix.

A={\begin{bmatrix} a_{1,1} & a_{1, 2} & ... & a_{1, n} \\ a_{2,1} & a_{2,2} & ... & a_{2,n} \\ ... & ... & ... & ... \\ a_{m,1} & a_{m,2} & ... & a_{m,n} \end{bmatrix}} \\ B={\begin{bmatrix} b_{1,1} & b_{1, 2} & ... & b_{1, p} \\ b_{2,1} & b_{2,2} & ... & b_{2,p} \\ ... & ... & ... & ... \\ b_{m,1} & b_{m,2} & ... & b_{m,p} \end{bmatrix}} \\ C=(A|B)=\begin{bmatrix} a_{1,1} & a_{1, 2} & ... & a_{1, n} &\bigm| & b_{1,1} & b_{1, 2} & ... & b_{1, p} \\ a_{2,1} & a_{2,2} & ... & a_{2,n} &\bigm| & b_{2,1} & b_{2,2} & ... & b_{2,p} \\ ... & ... & ... & ... &\bigm| & ... & ... & ... & ... \\ a_{m,1} & a_{m,2} & ... & a_{m,n} &\bigm| & b_{m,1} & b_{m,2} & ... & b_{m,p} \end{bmatrix}

So, if A and B are the following 3×3 and 3×1 matrices, then the augmented matrix C will be:

A={\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}} \\ B={\begin{bmatrix} 10 \\ 11 \\ 12 \end{bmatrix}} \\ C=(A|B)=\begin{bmatrix} 1 & 2 & 3 &\bigm| & 10 \\ 4 & 5 & 6 &\bigm| & 11 \\ 7 & 8 & 9 &\bigm| & 12 \end{bmatrix}

How to create an augmented matrix using Python NumPy?

We can use the following Python code to create an augmented matrix using NumPy…

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Amrita Mitra

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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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