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.

Introduzione all'idea della PCA

Cosa significa "Big Data"?

Individuare le ridondanze

L'algebra lineare alla base della PCA

Esplorando la covarianza

Standardizzare i tuoi dati

Calcoli di varianza/covarianza

Analisi agli autovalori dei dati combinati

Dov'è la varianza?

Eseguire la PCA in R

Scalare i dati prima della PCA

Riepilogare la PCA in R

Il subset cambia le cose?

Riepilogo

Principal Component Analysis

NFL Player dataset

WNBA Massey Matrix dataset

WNBA Point Differentials dataset

L'algebra lineare è uno degli strumenti più importanti della matematica applicata e della data science. In questo corso imparerai a lavorare con vettori e matrici, a risolvere equazioni matrice-vettore, a eseguire analisi di autovalori/autovettori e a usare la principal component analysis per ridurre la dimensionalità su insiemi di dati reali. Tutte le analisi saranno effettuate in R, uno dei linguaggi di programmazione più popolari al mondo.

Introduction to R

Corso di data science: introduzione all'algebra lineare, equazioni matrice-vettore, autovalori/vettori.

Algebra lineare per la Data Science in R

Questo corso è un'introduzione all'algebra lineare, uno dei temi matematici più importanti alla base della scienza dei dati.


Dov'è la varianza?

Algebra lineare per la Data Science in R

Esercizio pratico interattivo