Linear Algebra for Data Science — Vectors

Basic vector concepts used in data science and machine learning

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INTRODUCTION

After going through this article, the reader should learn the following:

• Definition of Vectors
• Perform addition and subtraction of vectors
• Perform scalar multiplication of vectors
• Use scalar multiplication for feature engineering
• Define dot product of vectors
• Use dot products to calculate correlation coefficient

To learn more about the use of matrices in data science and machine learning, see the article below:

Linear Algebra for Data Science — Matrices

Vectors

A vector is a one-dimensional collection of elements. The dimension of a vector n gives number of elements in the vector.

Addition and Subtraction of Vectors

Two vectors having same dimension can be added and subtracted.

Let vectors A and B be given as shown below:

Then the sum of A and B is given as

Scalar Multiplication of Vectors

Let c be a real number, then cA is the vector given by

Feature Engineering Using Scalar Multiplication