Learn how to code matrix algebra operations in R with the main C++ matrix algebra libraries: RcppArmadillo and RcppEigen.

Become an R Developer

This module aims to teach us how to code matrix algebra operations in R and with the main C++ matrix algebra libraries: RcppArmadillo and RcppEigen. Moreover, to clarify the matrix algebra operations, we’ll go through a simple algorithm to understand the computing implications. By the end of this module, we’ll have hands-on experience in performing matrix algebra computation in the R and Rcpp ecosystem, and the ability to develop algorithms for areas such as machine learning, image processing, and signal processing.

Computing Matrix Algebra with R and Rcpp

## Inverse definition

An $(𝑛 \times 𝑛)$ square matrix $𝐴$ is called **invertible** (also nonsingular or nondegenerate) if there exists an $(𝑛 \times 𝑛)$ square matrix $𝐵$ such that:

$$ 𝐴𝐵 = 𝐵𝐴 = 𝐼_𝑛 $$

- Here, $𝐼_𝑛$ denotes the $(𝑛 \times 𝑛)$ #key# identity matrix: a diagonal matrix where each element in the diagonal is equal to one. #key# where we use ordinary matrix multiplication. 

- If the matrix is invertible, then the matrix $𝐵$ is uniquely determined by $𝐴$ and is called the **inverse of $𝐴$**, denoted by $𝐴^{−1}$.

# Inverse definition

An $(𝑛 \times 𝑛)$ square matrix $𝐴$ is called **invertible** (also nonsingular or nondegenerate) if there exists an $(𝑛 \times 𝑛)$ square matrix $𝐵$ such that:

$$ 𝐴𝐵 = 𝐵𝐴 = 𝐼_𝑛 $$

- Here, $𝐼_𝑛$ denotes the $(𝑛 \times 𝑛)$ #key# identity matrix: a diagonal matrix where each element in the diagonal is equal to one. #key# where we use ordinary matrix multiplication. 

- If the matrix is invertible, then the matrix $𝐵$ is uniquely determined by $𝐴$ and is called the **inverse of $𝐴$**, denoted by $𝐴^{−1}$.

Learn how to invert a matrix using R, Rcpp, Armadillo, and Eigen.

Introduction

Assignment Operator

Addition of Matrices

Scalar Multiplication of Matrices

Multiplication of Matrices

Transposition of Matrices

Determinant of a Matrix

Inverse of a Matrix

System of Linear Equations

Conclusion

Matrix Inversion

Inverse definition