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Linear Algebra for Data Science in R

This course is an introduction to linear algebra, one of the most important mathematical topics underpinning data science.

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Course Description

Linear algebra is one of the most important set of tools in applied mathematics and data science. In this course, you’ll learn how to work with vectors and matrices, solve matrix-vector equations, perform eigenvalue/eigenvector analyses and use principal component analysis to do dimension reduction on real-world datasets. All analyses will be performed in R, one of the world’s most-popular programming languages.
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  1. 1

    Introduction to Linear Algebra

    Free

    In this chapter, you will learn about the key objects in linear algebra, such as vectors and matrices. You will understand why they are important and how they interact with each other.

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    Motivations
    50 xp
    Creating Vectors in R
    100 xp
    The Algebra of Vectors
    100 xp
    Creating Matrices in R
    100 xp
    Matrix-Vector Operations
    50 xp
    Matrix-Vector Compatibility
    50 xp
    Matrix Multiplication as a Transformation
    100 xp
    Reflections
    100 xp
    Matrix-Matrix Calculations
    50 xp
    Matrix Multiplication Compatibility
    50 xp
    Matrix Multiplication - Order Matters
    100 xp
    Intro to The Matrix Inverse
    100 xp
  2. 2

    Matrix-Vector Equations

    Many machine learning algorithms boil down to solving a matrix-vector equation. In this chapter, you learn what matrix-vector equations are trying to accomplish and how to solve them in R.

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    Motivation for Solving Matrix-Vector Equations
    50 xp
    The Meaning of Ax = b
    50 xp
    Exploring WNBA Data
    100 xp
    Matrix-Vector Equations - Some Theory
    50 xp
    Why is a Matrix Not Invertible?
    50 xp
    Understanding a Linear System's Three Outcomes
    50 xp
    Understanding the Massey Matrix
    50 xp
    Adjusting the Massey Matrix
    100 xp
    Inverting the Massey Matrix
    100 xp
    Solving Matrix-Vector Equations
    50 xp
    An Analogy with Regular Algebra
    50 xp
    2017 WNBA Ratings!
    100 xp
    Who Was the Champion?
    50 xp
    Other Considerations for Matrix-Vector Equations
    50 xp
    Other Methods for Matrix-Vector Equations
    50 xp
    Alternatives to the Regular Matrix Inverse
    100 xp
  3. 3

    Eigenvalues and Eigenvectors

    Matrix operations are complex. Eigenvalue/eigenvector analyses allow you to decompose these operations into simpler ones for the sake of image recognition, genomic analysis, and more!

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    Intro to Eigenvalues and Eigenvectors
    50 xp
    Interpreting Scalar Multiplication
    50 xp
    Scaling Different Axes
    100 xp
    Definition of Eigenvalues and Eigenvectors
    50 xp
    Why "Eigen"?
    50 xp
    Finding Eigenvalues in R
    100 xp
    Scalar Multiplies of Eigenvectors are Eigenvectors
    100 xp
    Computing Eigenvalues and Eigenvectors in R
    50 xp
    How Many Eigenvalues?
    50 xp
    Verifying the Math on Eigenvalues
    100 xp
    Computing Eigenvectors in R
    100 xp
    Some More on Eigenvalues and Eigenvectors
    50 xp
    Eigenvalue Ordering
    50 xp
    Markov Models for Allele Frequencies
    100 xp
  4. 4

    Principal Component Analysis

    “Big Data” is ubiquitous in data science and its applications. However, redundancy in these datasets can be problematic. In this chapter, we learn about principal component analysis and how it can be used in dimension reduction.

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    Intro to the Idea of PCA
    50 xp
    What Does "Big Data" Mean?
    50 xp
    Finding Redundancies
    100 xp
    The Linear Algebra Behind PCA
    50 xp
    Covariance Explored
    50 xp
    Standardizing Your Data
    100 xp
    Variance/Covariance Calculations
    100 xp
    Eigenanalyses of Combine Data
    100 xp
    Where's the Variance?
    50 xp
    Performing PCA in R
    50 xp
    Scaling Data Before PCA
    100 xp
    Summarizing PCA in R
    100 xp
    Does Subsetting Change Things?
    50 xp
    Wrap-Up
    50 xp
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datasets

NFL Player datasetWNBA Massey Matrix datasetWNBA Point Differentials dataset

collaborators

Collaborator's avatar
Chester Ismay
Collaborator's avatar
David Campos
Collaborator's avatar
Shon Inouye

prerequisites

Introduction to R
Eric Eager HeadshotEric Eager

VP of Research and Development at SumerSports

Eric Eager is the VP of R&D at SumerSports. Prior to joining Sumer in 2022, he ran R&D at Pro Football Focus, where he analyzed data for all 32 National Football League teams and over 130 college football teams, along with every major media entity and thousands of subscribers. From 2012-2018 he was a professor in the Department of Mathematics and Statistics at the University of Wisconsin – La Crosse, where he published over 25 papers in mathematical biology and the scholarship of teaching and learning while securing more than $300,000 in National Science Foundation funding for undergraduate mentorship.
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