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.

Motivations

Creating Vectors in R

The Algebra of Vectors

Creating Matrices in R

Matrix-Vector Operations

Matrix-Vector Compatibility

Matrix Multiplication as a Transformation

Reflections

Matrix-Matrix Calculations

Matrix Multiplication Compatibility

Matrix Multiplication - Order Matters

Intro to The Matrix Inverse

Introduction to Linear Algebra

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.

Motivation for Solving Matrix-Vector Equations

The Meaning of Ax = b

Exploring WNBA Data

Matrix-Vector Equations - Some Theory

Why is a Matrix Not Invertible?

Understanding a Linear System's Three Outcomes

Understanding the Massey Matrix

Adjusting the Massey Matrix

Inverting the Massey Matrix

Solving Matrix-Vector Equations

An Analogy with Regular Algebra

2017 WNBA Ratings!

Who Was the Champion?

Other Considerations for Matrix-Vector Equations

Other Methods for Matrix-Vector Equations

Alternatives to the Regular Matrix Inverse

Matrix-Vector Equations

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!

Intro to Eigenvalues and Eigenvectors

Interpreting Scalar Multiplication

Scaling Different Axes

Definition of Eigenvalues and Eigenvectors

Why "Eigen"?

Finding Eigenvalues in R

Scalar Multiplies of Eigenvectors are Eigenvectors

Computing Eigenvalues and Eigenvectors in R

How Many Eigenvalues?

Verifying the Math on Eigenvalues

Computing Eigenvectors in R

Some More on Eigenvalues and Eigenvectors

Eigenvalue Ordering

Markov Models for Allele Frequencies

Eigenvalues and Eigenvectors

“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.

Introductie tot het idee achter PCA

Wat betekent "Big Data"?

Redundantie opsporen

De lineaire algebra achter PCA

Covariantie onder de loep

Je gegevens standaardiseren

Variantie-/covariantie-berekeningen

Eigenanalyses van gecombineerde data

Waar zit de variantie?

PCA uitvoeren in R

Data schalen vóór PCA

PCA samenvatten in R

Verandert subsetten iets?

Afronding

Principal Component Analysis

NFL Player dataset

WNBA Massey Matrix dataset

WNBA Point Differentials dataset

Lineaire algebra is een van de belangrijkste hulpmiddellensets in de toegepaste wiskunde en data science. In deze cursus leer je werken met vectoren en matrices, matrix-vectorvergelijkingen oplossen, analyses met eigenwaarden en eigenvectoren uitvoeren en principal component analysis gebruiken om dimensiereductie toe te passen op realistische gegevenssets. Alle analyses worden uitgevoerd in R, een van de populairste programmeertalen ter wereld.

Introduction to R

Deze cursus datawetenschap introduceert lineaire algebra, matrix-vectorvergelijkingen en PCA.

Lineaire algebra voor data science in R

Deze cursus is een inleiding tot lineaire algebra, een van de belangrijkste wiskundige onderwerpen die ten grondslag liggen aan datawetenschap.


Covariantie onder de loep

Lineaire algebra voor data science in R

Praktische interactieve oefening