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.

Pengantar Gagasan PCA

Apa Arti "Big Data"?

Menemukan Redundansi

Aljabar Linear di Balik PCA

Menjelajahi Kovarians

Standarisasi Data Anda

Perhitungan Varians/Kovarians

Analisis Eigen atas Data Gabungan

Di Mana Variansnya?

Melakukan PCA di R

Menskalakan Data Sebelum PCA

Merangkum PCA di R

Apakah Subsetting Mengubah Hasil?

Penutup

Principal Component Analysis

NFL Player dataset

WNBA Massey Matrix dataset

WNBA Point Differentials dataset

Aljabar linear adalah salah satu seperangkat alat terpenting dalam matematika terapan dan data science. Di kursus ini, Anda akan belajar bekerja dengan vektor dan matriks, menyelesaikan persamaan matriks-vektor, melakukan analisis eigenvalue/eigenvector, dan menggunakan principal component analysis untuk melakukan reduksi dimensi pada himpunan data dunia nyata. Semua analisis akan dilakukan di R, salah satu bahasa pemrograman paling populer di dunia.

Introduction to R

Kursus ini memperkenalkan aljabar linier: persamaan matriks-vektor, analisis eigen, dan PCA.

Aljabar Linear untuk Data Science di R

Mata kuliah ini merupakan pengenalan terhadap aljabar linier, salah satu topik matematika paling penting yang mendasari ilmu data.


Di Mana Variansnya?

Aljabar Linear untuk Data Science di R

Latihan interaktif praktis