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!

Introduzione ad autovalori e autovettori

Interpretare la moltiplicazione per uno scalare

Scalare assi diversi

Definizione di autovalori e autovettori

Perché "Eigen"?

Trovare autovalori in R

I multipli scalari degli autovettori sono autovettori

Calcolare autovalori e autovettori in R

Quanti autovalori?

Verificare la matematica sugli autovalori

Calcolare gli autovettori in R

Ancora sugli autovalori e autovettori

Ordinamento dei valori propri

Modelli di Markov per le frequenze alleliche

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.

Intro to the Idea of PCA

What Does "Big Data" Mean?

Finding Redundancies

The Linear Algebra Behind PCA

Covariance Explored

Standardizing Your Data

Variance/Covariance Calculations

Eigenanalyses of Combine Data

Where's the Variance?

Performing PCA in R

Scaling Data Before PCA

Summarizing PCA in R

Does Subsetting Change Things?

Wrap-Up

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.


Ordinamento dei valori propri

Algebra lineare per la Data Science in R

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