How to create a row vector and a column vector using Python NumPy?

by | Oct 3, 2023 | Linear Algebra

Create Row Vectors And Column Vectors

What are scalars and vectors in linear algebra?

In linear algebra, a scalar is a single number that can scale or stretch a matrix or a vector. For example, the numbers 2, -3, 1.2 are all scalars.

A vector, on the other hand, is a list of numbers. And the number of numbers in a vector is called the dimensionality of the vector. So, an n-dimensional vector is a list of n numbers. For example, v1 is a 3 dimensional vector.

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

Please note that the ordering of numbers in a vector is important. So, v1 and v2 are not the same vector.

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

A vector can be represented with a 1xn or a nx1 matrix. When a vector is represented with n numbers in a single row, the vector is called a row vector. For example, v3 is a row vector.

\overrightarrow{v3} = \begin{bmatrix} 1 & 2 & 3 \end{bmatrix}

On the other hand, when a vector is represented with a single column containing n numbers, we call the vector a column vector. For example, v4 is a column vector.

\overrightarrow{v4} = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}

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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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