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Computing Matrix Algebra with R and Rcpp

Gain insights into coding matrix algebra operations in R and Rcpp. Explore matrix summation, multiplication, LU factorization, and eigendecomposition. Discover applications in machine learning, signal and image processing.

Intermediate

38 Lessons

19h

Certificate of Completion

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Explanations

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This course includes

61 Playgrounds

12 Quizzes

Course Overview

What You'll Learn

Course Content

Course Overview

Matrix algebra is the foundation for machine learning, signal processing, image processing, and many other popular algorithms. It is very important that aspiring computer scientists get a solid understanding of the subject, and there’s no better way to achieve this than coding matrix algebra operations. The course aims to teach you how to code matrix algebra operations in R, and with main C++ matrix algebra libraries: RcppArmadillo and RcppEigen. Moreover, to clarify the matrix algebra operations, a simpl...Show More

What You'll Learn

An understanding of introductory matrix algebra

Working knowledge of coding matrix algebra operations in R

Ability to implement simple matrix algebra algorithm in Rcpp

Hands on experience of using RcppArmadillo and RcppEigen in R

An understanding of introductory matrix algebra

Course Content

Introduction

1 Lessons

Get familiar with practical matrix algebra computation using R, Rcpp, and C++ libraries.

Get Started with Matrix Algebra

Assignment Operator

3 Lessons

Get started with matrix assignments in R and Rcpp, plus a hands-on challenge.

Assignment Operations on Matrices

Quiz: Matrix Assignment

Challenge: Matrix Assignment

Addition of Matrices

3 Lessons

Break apart the principles of matrix addition and reinforce through quizzes and challenges.

Matrix Addition

Quiz: Matrix Addition

Challenge: Matrix Addition

Scalar Multiplication of Matrices

3 Lessons

Build a foundation in scalar multiplication of matrices with R and Rcpp.

Scalar Multiplication

Quiz: Scalar Multiplication

Challenge: Scalar Multiplication

Multiplication of Matrices

3 Lessons

Solve problems in matrix multiplication with R and Rcpp through practical exercises and quizzes.

Multiplication Operation on Matrices

Quiz: Matrix Multiplication

Challenge: Matrix Multiplication

Transposition of Matrices

3 Lessons

Tackle transposing matrices in R and C++, assessing understanding, and checking symmetry.

Matrix Transposition

Quiz: Matrix Transposition

Challenge: Matrix Transposition

Determinant of a Matrix

3 Lessons

Practice using tools to calculate, interpret, and analyze matrix determinants efficiently.

Determinant of a Matrix

Quiz: Matrix Determinant

Challenge: Matrix Determinant

Inverse of a Matrix

3 Lessons

Learn how to use R to compute and verify matrix inversions effectively.

Matrix Inversion

Quiz: Matrix Inversion

Challenge: Matrix Inversion

System of Linear Equations

3 Lessons

Solve challenges with linear equations using R and C++, including quizzes and coding tasks.

System of Linear Equations Solution

Quiz: System of Linear Equations

Challenge: System of Linear Equations

10.

LU Matrix Factorization

3 Lessons

Go hands-on with LU matrix factorization to decompose matrices and efficiently solve linear systems.

LU Matrix Factorization

Quiz: LU Matrix Factorization

Challenge: LU Matrix Factorization

11.

Cholesky Factorization

3 Lessons

Break down complex ideas of Cholesky factorization, tests, and practical challenges in R.

Cholesky Factorization

Quiz: Cholesky Factorization

Challenge: Cholesky Factorization

12.

QR Matrix Factorization

3 Lessons

Solve problems in QR factorization, validate with quizzes, and implement coding challenges.

QR Factorization

Quiz: QR Matrix Factorization

Challenge: QR Matrix Factorization

13.

Eigendecomposition

3 Lessons

See how it works to decompose matrices into eigenvalues and eigenvectors using R and Rcpp.

Eigendecomposition of a Matrix

Quiz: Eigendecomposition

Challenge: Eigendecomposition

14.

Wrapping It Up

1 Lessons

Build on knowledge of matrix algebra and R for future learning opportunities.

Conclusion

Course Author

Mario De Toma

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