# Linear Algebra for Data Science — Matrices

## Basic matrix 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 Matrices
- Matrix multiplication
- Apply matrix multiplication to linear regression
- Inverse of a matrix
- Eigenvalues
- Eigenvectors

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

# Matrices

A matrix is a two-dimensional collection of elements. A matrix is represented by its number of rows and columns. For example, an *n x m* matrix ** A **has

*n*rows and

*m*columns:

## Matrix Multiplication

Matrix multiplication plays an important role in data science and machine learning. For matrix multiplication between two matrices to be well defined, the two matrices must be compatible, that is, the number of columns of matrix **A** must be equal to the number of rows of matrix **B**. Matrix multiplication is not commutative, that is **AB** in not equal to **BA**.

Let **A **be an *n x p* matrix, and **B **a *p x m* matrix

Then the product matrix **C = AB **is an *n x m *matrix with elements given as