How to multiply a matrix and a vector using Python NumPy?

by | Oct 3, 2023 | Linear Algebra

Matrix-Vector Multiplication

What are scalars and vectors in linear algebra?

A scalar in linear algebra is a single number that can scale or stretch a vector or matrix. For example, 1, 2.3, -4, etc. are scalars.

On the other hand, a vector in linear agebra is a list of numbers. The number of numbers in a vector is called the dimensionality of the vector. For example, v1 and v2 here are two vectors that are 2 and 3 dimensional, respectively.

\vec{v1}={\begin{bmatrix} 1 & 2 \end{bmatrix}} \\ \vec{v2}={\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}}

Please note that the ordering of numbers in a vector is important. For example, the vectors v3 and v4 are not the same.

\vec{v3}={\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}} \\ \vec{v4}={\begin{bmatrix} 1 \\ 3 \\ 2 \end{bmatrix}}

Moreover, a row vector is a vector that can be represented 1xn matrix. In other words, a row vector will have a single row and n number of column for some number n.

On the other hand, a column vector is a vector that can be represented with a nx1 matrix. So, a column vector is a vector that has n number of rows and a single column for some n.

For example, v5 is a row vector and v6 is a column vector.

\vec{v5}={\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}} \\ \vec{v6}={\begin{bmatrix} 1 \\ 2 \\ 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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