Package index • matlib

Package description

matlib-package matlib _PACKAGE: matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics.

Convenience functions

Simple functions for matrix algebra oparations

J(): Create a vector, matrix or array of constants

len(): Length of a Vector or Column Lengths of a Matrix

mpower(): Matrix Power

Proj(): Projection of Vector y on columns of X

R(): Rank of a Matrix

symMat(): Create a Symmetric Matrix from a Vector

tr(): Trace of a Matrix

vec(): Vectorize a Matrix

xprod(): Generalized Vector Cross Product

Determinants

Functions for calculating determinants by cofactor expansion

adjoint(): Calculate the Adjoint of a matrix

cofactor(): Cofactor of A[i,j]

Det(): Determinant of a Square Matrix

minor(): Minor of A[i,j]

rowCofactors(): Row Cofactors of A[i,]

rowMinors(): Row Minors of A[i,]

Elementary row operations

Functions for solving linear equations “manually” by the steps used in row echelon form and Gaussian elimination

rowadd(): Elementary Row Operations

rowmult(): Multiply Rows by Constants

rowswap(): Interchange two rows of a matrix

buildTmat() as.matrix(<trace>) print(<trace>): Build/Get transformation matrices

Linear equations

Functions to illustrate linear equations of the form $\mathbf{A x = b}$

showEqn(): Show Matrices (A, b) as Linear Equations

plotEqn(): Plot Linear Equations

plotEqn3d(): Plot Linear Equations in 3D

Solve(): Solve and Display Solutions for Systems of Linear Simultaneous Equations

printMatEqn(): Print Matrices or Matrix Operations Side by Side

printMatrix(): (Deprecated) Print a matrix, allowing fractions or LaTeX output

LaTeX matrices

Create and manipulate LaTeX repesentations of matrices and matrix equations

matrix2latex(): (Deprecated) Convert matrix to LaTeX equation

latexMatrix() partition() getLatex() getBody() getWrapper() Dim() Nrow() Ncol() print(<latexMatrix>) is.numeric(<latexMatrix>) as.double(<latexMatrix>) `[`(<latexMatrix>) cbind(<latexMatrix>) rbind(<latexMatrix>) dimnames(<latexMatrix>) `Dimnames<-`() `Rownames<-`() `Colnames<-`(): Create and Manipulate LaTeX Representations of Matrices

matsum() `+`(<latexMatrix>) matdiff() `-`(<latexMatrix>) `*`(<latexMatrix>) Dot() matmult() `%*%`(<latexMatrix>) matpower() `^`(<latexMatrix>) inverse() t(<latexMatrix>) determinant(<latexMatrix>) solve(<latexMatrix>) kronecker(<latexMatrix>,<latexMatrix>) `%X%`: Various Functions and Operators for "latexMatrix" Objects

Eqn() ref(): Create a LaTeX Equation Wrapper

overset() underset() overbrace() underbrace() Eqn_overset() Eqn_underset() Eqn_overbrace() Eqn_underbrace() Eqn_newline() newline() Eqn_text() Eqn_hspace() hspace() Eqn_vspace() vspace() Eqn_size() size(): Helpers to Compose Equations with Eqn

Gaussian elimination

Functions for illustrating Gaussian elimination

cholesky(): Cholesky Square Root of a Matrix

echelon(): Echelon Form of a Matrix

gaussianElimination() print(<enhancedMatrix>): Gaussian Elimination

Ginv(): Generalized Inverse of a Matrix

Inverse(): Inverse of a Matrix

LU(): LU Decomposition

MoorePenrose(): Moore-Penrose inverse of a matrix

QR(): QR Decomposition by Graham-Schmidt Orthonormalization

swp(): The Matrix Sweep Operator

Eigenvalues

Functions to illustrate the algorithms for calculating eigenvalues and eigenvectors

Eigen(): Eigen Decomposition of a Square Symmetric Matrix

powerMethod(): Power Method for Eigenvectors

showEig(): Show the eigenvectors associated with a covariance matrix

SVD(): Singular Value Decomposition of a Matrix

Vector diagrams

Functions for drawing vector diagrams in 2D and 3D

angle(): Angle between two vectors

arc(): Draw an arc showing the angle between vectors

arrows3d(): Draw 3D arrows

circle(): Draw circles on an existing plot.

circle3d(): Draw a horizontal circle

cone3d(): Draw a 3D cone

corner(): Draw a corner showing the angle between two vectors

getYmult(): Correct for aspect and coordinate ratio

pointOnLine(): Position of a point along a line

regvec3d(): Vector space representation of a two-variable regression model

plot(<regvec3d>) summary(<regvec3d>) print(<regvec3d>): Plot method for regvec3d objects

vectors(): Draw geometric vectors in 2D

vectors3d(): Draw 3D vectors

Other

Other functions in the package, unclassified

matrix2latex(): (Deprecated) Convert matrix to LaTeX equation

GramSchmidt(): Gram-Schmidt Orthogonalization of a Matrix

gsorth(): Gram-Schmidt Orthogonalization of a Matrix

svdDemo(): Demonstrate the SVD for a 3 x 3 matrix

vandermode(): Vandermode Matrix

Data

Some small data sets used in examples

class: Class Data Set

coffee: Data on Coffee, Stress and Heart Damage

therapy: Therapy Data

workers: Workers Data