Data Science Texts

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Linear Algebra

Strongly Recommended Prerequisites

Recommended Prerequisites

Last Updated: 7/18/2019

Linear algebra is ostensibly the mathematics used to solve linear equations, but in practice it is the generalization of basic algebra to multi-dimensional objects. Since multivariate objects are of great importance in data science, linear algebra is an essential tool for any data scientist. Many find linear algebra a dull subject, but proficiency is required for more advanced topics. So, even if you can't find beauty in linear algebra, know that the effort you put into mastering it will be rewarded in other data science disciplines.

Visualization of Some Common Linear Transformations

Many simple visual transformations can be encoded as matrix transforms. Adopting the formalism of linear algebra allows practitioners to perform such transformations easily, facilitates analysis, makes composition trivial, and suggests decompositions that may lead to greater understanding.

Recommended Books

  1. Introduction to Linear Algebra

    W. Gilbert Strang

    Check it out on Amazon!

    Key Features

    Key Topics

    • Complex Vectors
    • Determinants
    • Eigenvalues and Eigenvectors
    • Fast Fourier Transform
    • Inverse Matrices
    • Linear Equations
    • Linear Programming
    • Linear Transformations
    • Projections
    • Singular Value Decomposition
    • Vector Spaces
    • Vectors

    Description

    If you have never studied linear algebra before, this is the book for you. Frankly, there are more coherent linear algebra books than this one. However, the most important aspect of learning linear algebra is practicing with exercises, and this book comes with an extensive collection. Plus, there are solutions available on the book's website. Strang's book is also associated with a set of video lectures and other supplementary material available here. The applications chapter is excellent. It includes: graphs and networks, linear programming, Fourier series, computer graphics, cryptography, and more.

  2. Linear Algebra Done Right

    Sheldon J. Axler

    Check it out on Amazon!

    Key Features

    Key Topics

    • Determinants
    • Duality
    • Eigenvalues and Eigenvectors
    • Inner Product Spaces
    • Invertibility
    • Linear Maps
    • Operators on Various Spaces
    • Polynomials
    • Singular Value Decomposition
    • Spectral Theorem
    • Vector Spaces

    Description

    Linear Algebra Done Right is a much more pure math take on linear algebra than typical texts. We don't recommend this book as a first look for the purposes of data science. However, if you have studied linear algebra already and want a more rigorous and mathematical book than the typical applied text, Axler is a great option. If you find determinants unintuitive, you'll be pleased that this book largely avoids using them.