How to perform vector addition and subtraction using Python NumPy?

by | Oct 3, 2023 | Linear Algebra

Vector Addition And Subtraction

How to perform vector addition and subtraction?

Let’s say v1 and v2 are two row vectors with the same dimension. If we add the two vectors v1 and v2, then we will get another vector v3 that will have the same dimension as v1 and v2. And each component of v3 will be the addition of the corresponding components of v1 and v2.

Let’s look at an example.

\overrightarrow{v1} = \begin{bmatrix} 4 & 5 & 6 \end{bmatrix} \\ \overrightarrow{v2} = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \\ \overrightarrow{v3} = \overrightarrow{v1} + \overrightarrow{v2} \\ =\begin{bmatrix} 4 & 5 & 6 \end{bmatrix} + \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \\ =\begin{bmatrix} 5 & 7 & 9 \end{bmatrix}

Similarly, let’s say v4 and v5 are two column vectors of the same dimension. We can add these two vectors to get another column vector v6 of the same dimension as v4 and v5.

\overrightarrow{v4} = \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} \\ \overrightarrow{v5} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \\ \overrightarrow{v6} = \overrightarrow{v4} + \overrightarrow{v5} \\ =\begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} + \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \\ =\begin{bmatrix} 5 \\ 7 \\ 9 \end{bmatrix}

Similarly, we can subtract these vectors. For example, we can subtract the vector v2 from v1 to get the vector v7.

\overrightarrow{v1} = \begin{bmatrix} 4 & 5 & 6 \end{bmatrix} \\ \overrightarrow{v2} = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \\ \overrightarrow{v7} = \overrightarrow{v1} - \overrightarrow{v2} \\ =\begin{bmatrix} 4 & 5 & 6 \end{bmatrix} - \begin{bmatrix} 1 & 2 & 3 \end{bmatrix} \\ =\begin{bmatrix} 3 & 3 & 3 \end{bmatrix}

And we can subtract the column vector v5 from the vector v4 to get another column vector v8.

\overrightarrow{v4} = \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} \\ \overrightarrow{v5} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \\ \overrightarrow{v8} = \overrightarrow{v4} - \overrightarrow{v5} \\ =\begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix} - \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \\ =\begin{bmatrix} 3 \\ 3 \\ 3 \end{bmatrix}

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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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