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.

Motivasi untuk Menyelesaikan Persamaan Matriks-Vektor

Makna dari Ax = b

Menjelajahi Data WNBA

Persamaan Matriks-Vektor - Beberapa Teori

Mengapa Suatu Matriks Tidak Dapat Diinvers?

Memahami Tiga Kemungkinan Hasil Sistem Linear

Memahami Matriks Massey

Menyesuaikan Matriks Massey

Membalik Matriks Massey

Menyelesaikan Persamaan Matriks–Vektor

Analogi dengan Aljabar Biasa

Peringkat WNBA 2017!

Siapa Juaranya?

Pertimbangan Lain untuk Persamaan Matriks–Vektor

Metode Lain untuk Persamaan Matriks-Vektor

Alternatif untuk Invers Matriks Biasa

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.

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

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.


Pertimbangan Lain untuk Persamaan Matriks–Vektor

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