matlib

Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Version 0.5.2

These functions are mainly for tutorial purposes in learning matrix algebra ideas using R. In some cases, functions are provided for concepts available elsewhere in R, but where the function call or name is not obvious. In other cases, functions are provided to show or demonstrate an algorithm.

Installation

Get the released version from CRAN:

 install.packages("matlib")

The development version can be installed to your R library directly from this repo via:

 if (!require(devtools)) install.packages("devtools")
 library(devtools)
 install_github("friendly/matlib")

This installs the package from the source, so you will need to have R Tools installed on your system. R Tools for Windows takes you to the download page for Windows. R Tools for Mac OS X has the required programs for Mac OS X.

Alternatively, a Windows binary (not always current) is available at http://www.psych.yorku.ca/lab/psy6140/R/matlib.zip and can be installed via

install.packages("http://www.psych.yorku.ca/lab/psy6140/R/matlib.zip", repos=NULL)

This will usually be more current than the CRAN version, but less current than the GitHub version.

Contents

1. Convenience functions:

• tr() - trace of a matrix
• R() - rank of a matrix
• len() - Euclidean length of a vector or columns of a matrix
• Proj(y, X) - projection of vector y on colunms of X
• mpower(A, p) - matrix powers for a square symmetric matrix
• vectors() - plot geometric vectors

2. Determinants: functions for calculating determinants by cofactor expansion

• minor() - Minor of A[i,j]
• cofactor() - Cofactor of A[i,j]
• row_minors() - Row minors of A[i,]
• row_cofactors() - Row cofactors of A[i,]

3. Elementary row operations: functions for solving linear equations "manually" by the steps used in row echelon form and Gaussian elimination

• rowadd() - Add multiples of rows to other rows
• rowmult() - Multiply rows by constants
• rowswap() - Interchange two rows of a matrix

4. Linear equations: functions to illustrate linear equations of the form A x = b

• showEqn(A, b) - show matrices (A, b) as linear equations
• plotEqn(A, b), plotEqn3d(A, b) - plot matrices (A, b) as linear equations

5. Gaussian elimination: functions for illustrating Gaussian elimination for solving systems of linear equations of the form A x = b. These functions provide a verbose=TRUE argument to show the intermediate steps.

• gaussianElimination(A, B) - reduces (A, B) to (I, A^{-1} B)
• Inverse(X), inv() - uses gaussianElimination to find the inverse of X
• echelon(X) - uses gaussianElimination to find the reduced echelon form of X
• Ginv(X) - uses gaussianElimination to find the generalized inverse of X
• cholesky() - calculates a Cholesky square root of a matrix
• swp() - matrix sweep operator

6. Eigenvalues -- functions to illustrate the algorithms for calculating eigenvalues and eigenvectors

• eig() - eigenvalues and eigenvectors
• SVD() - singular value decomposition

Vignettes

A small collection of vignettes is now available. Use browseVignettes("matlib") to see them.