Perform matrix multiplication using Python NumPy

by | Oct 3, 2023 | Linear Algebra

Perform Matrix Multiplication Using NumPy

Let’s say A is an mxn matrix and B is an nxp matrix. If we multiply these two matrices, we will get another matrix C such that:

C_{i,j}=\sum_{m}{A_{i,m}B_{m,j}}

Here, Ci,j indicates the element in the ith row and jth column of matrix C. Similarly, Ai,m indicates the element in the ith row and mth column of matrix A. And Bm,j indicates the element in the mth row and jth column of the matrix B.

Please note that two matrices A and B can multiplied only when the number of columns of matrix A is equal to the number of rows of matrix B. And if A is an mxn matrix and B is an nxp matrix, then after multiplying A and B we will get an mxp matrix.

Let’s look at an example. Let’s say A and B are two matrices with the following elements.

A={\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}} \\ B={\begin{bmatrix} 7 & 8 & 9 \\ 10 & 11 & 612 \\ 13 & 14 & 15 \end{bmatrix}}

So, if we multiply A and B, we will get another matrix C, such that:

C=A \times B={\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix}} \times {\begin{bmatrix} 7 & 8 & 9 \\ 10 & 11 & 612 \\ 13 & 14 & 15 \end{bmatrix}} \\ ={\begin{bmatrix} 1 \times 7 + 2 \times 10 + 3 \times 13 & 1 \times 8 + 2 \times 11 + 3 \times 14 & 1 \times 9 + 2 \times 12 + 3 \times 15 \\ 4 \times 7 + 5 \times 10 + 6 \times 13 & 4 \times 8 + 5 \times 11 + 6 \times 14 & 4 \times 9 + 5 \times 12 + 6 \times 15 \end{bmatrix}} \\ ={\begin{bmatrix} 66 & 72 & 78 \\ 156 & 171 & 186 \end{bmatrix}}

Please note that here A is a 2×3 matrix and B is a 3×3 matrix. So, after multiplying A and B we get a 2×3 matrix.

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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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