Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics, http://friendly.github.io/matlib/
Version 0.9.4
These functions are mainly for tutorial purposes in teaching & learning matrix algebra ideas using R. In some cases, functions are provided for concepts or computations available elsewhere in R, but where the name is not obvious. In other cases, we provide cover functions to show or demonstrate an algorithm in more detail, sometimes providing a verbose =
argument to print the details of computations.
In addition, a collection of functions are provided for drawing vector diagrams in 2D and 3D, illustrating various concepts of linear algebra more concretely than has been available before.
Get the released version from CRAN:
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", build_vignettes = TRUE)
This installs the package from the source and creates the package vignettes, 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.
The functions in this package are grouped under the following topics
tr()
- trace of a matrixR()
- rank of a matrixJ()
- constant vector, matrix or arraylen()
- Euclidean length of a vector or columns of a matrixvec()
- vectorize a matrixProj(y, X)
- projection of vector y on columns of Xmpower(A, p)
- matrix powers for a square symmetric matrixxprod(...)
- vector cross-productminor()
- Minor of A[i,j]cofactor()
- Cofactor of A[i,j]rowMinors()
- Row minors of A[i,]rowCofactors()
- Row cofactors of A[i,]Det()
- Determinants by elimination or eigenvaluesrowadd()
- Add multiples of rows to other rowsrowmult()
- Multiply rows by constantsrowswap()
- Interchange two rows of a matrixshowEqn(A, b)
- show matrices (A, b) as linear equationsplotEqn(A, b)
, plotEqn3d(A, b)
- plot matrices (A, b) as linear equationsverbose=TRUE
argument to show the intermediate steps and a fractions=TRUE
argument to show results using MASS::fractions
.gaussianElimination(A, B)
- reduces (A, B) to (I, A^{-1} B)Inverse(X)
, inv()
- uses gaussianElimination
to find the inverse of Xechelon(X)
- uses gaussianElimination
to find the reduced echelon form of XGinv(X)
- uses gaussianElimination
to find the generalized inverse of XLU(X)
- LU decomposition of a matrix Xcholesky()
- calculates a Cholesky square root of a matrixswp()
- matrix sweep operatorEigen()
- eigenvalues and eigenvectorsSVD()
- singular value decompositionpowerMethod()
- find the dominant eigenvector using the power methodshowEig()
- draw eigenvectors on a 2D scatterplot with a dataEllipseMoorePenrose()
- illustrates how the Moore-Penrose inverse can be calculated using SVD()
arrows3d()
- draw nice 3D arrowscorner()
, arc()
- draw a corner or arc showing the angle between two vectors in 2D/3DpointOnLine()
- position of a point along a linevectors()
, vectors3d()
- plot geometric vector diagrams in 2D/3Dregvec3d()
- calculate and plot vectors representing a bivariate regression model, lm(y ~ x1 + x2)
in mean-deviation form.A small collection of vignettes is now available. Use browseVignettes("matlib")
to explore them.
Vignette | Title |
---|---|
det-ex1 | Properties of determinants |
det-ex2 | Evaluation of determinants |
inv-ex1 | Inverse of a matrix |
inv-ex2 | Matrix inversion by elementary row operations |
ginv | Generalized inverse |
eigen-ex1 | Eigenvalues and Eigenvectors: Properties |
eigen-ex2 | Eigenvalues: Spectral Decomposition |
linear-equations | Solving Linear Equations |
gramreg | Gram-Schmidt Orthogonalization and Regression |
data-beta | Vector Spaces of Least Squares and Linear Equations |
See also: Fox & Friendly, Visualizing Simultaneous Linear Equations, Geometric Vectors, and Least-Squares Regression with the matlib Package for R, June 2016, useR! Conference, Stanford.