Practical Linear Algebra for Data Science

Chapter 5. Matrices, Part 1

A matrix is a vector taken to the next level. Matrices are highly versatile mathematical objects. They can store sets of equations, geometric transformations, the positions of particles over time, financial records, and myriad other things. In data science, matrices are sometimes called data tables, in which rows correspond to observations (e.g., customers) and columns correspond to features (e.g., purchases).

This and the following two chapters will take your knowledge about linear algebra to the next level. Get a cup of coffee and put on your thinking cap. Your brain will be bigger by the end of the chapter.

Creating and Visualizing Matrices in NumPy

Depending on the context, matrices can be conceptualized as a set of column vectors stacked next to each other (e.g., a data table of observations-by-features), as a set of row vectors layered on top of each other (e.g., multisensor data in which each row is a time series from a different channel), or as an ordered collection of individual matrix elements (e.g., an image in which each matrix element encodes pixel intensity value).

Visualizing, Indexing, and Slicing Matrices

Small matrices can simply be printed out in full, like the following examples:

$$\left[\begin{array}{cc}1& 2\\ \pi & 4\\ 6& 7\end{array}\right],\left[\begin{array}{cc}-6& \mathrm{1/3}\\ e^{4.3}& -1.4\\ \mathrm{6/5}& 0\end{array}\right]$$

But that’s not scalable, and matrices that you work with in practice can be large, perhaps containing billions of elements. Therefore, larger matrices ...