Package: matlib 1.0.1

matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

A collection of matrix functions for teaching and learning matrix linear algebra as used in multivariate statistical methods. Many of these functions are designed 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. In addition, a collection of functions are provided for drawing vector diagrams in 2D and 3D and for rendering matrix expressions and equations in LaTeX.

Authors:Michael Friendly [aut, cre], John Fox [aut], Phil Chalmers [aut], Georges Monette [ctb], Gaston Sanchez [ctb]

matlib_1.0.1.tar.gz
matlib_1.0.1.zip(r-4.7)matlib_1.0.1.zip(r-4.6)matlib_1.0.1.zip(r-4.5)
matlib_1.0.1.tgz(r-4.6-any)matlib_1.0.1.tgz(r-4.5-any)
matlib_1.0.1.tar.gz(r-4.7-any)matlib_1.0.1.tar.gz(r-4.6-any)
matlib_1.0.1.tgz(r-4.6-emscripten)
manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
matlib/json (API)

# Install 'matlib' in R:
install.packages('matlib', repos = c('https://friendly.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/friendly/matlib/issues

Pkgdown/docs site:https://friendly.github.io

Datasets:

On CRAN:

Conda:

diagramslinear-equationsmatrixmatrix-functionsmatrix-visualizervectorvignette

11.98 score 71 stars 14 packages 1.1k scripts 7.9k downloads 1 mentions 96 exports 94 dependencies

Last updated from:c7977ded6c. Checks:9 OK. Indexed: yes.

TargetResultTimeFilesSyslog
linux-devel-x86_64OK205
source / vignettesOK280
linux-release-x86_64OK192
macos-release-arm64OK111
macos-oldrel-arm64OK146
windows-develOK114
windows-releaseOK113
windows-oldrelOK116
wasm-releaseOK166

Exports:%X%adjointanglearcarrows3dbuildTmatcholeskycirclecircle3dcofactorColnames<-cone3dcornerDetDimDimnames<-DotechelonEigenEqnEqn_hspaceEqn_newlineEqn_overbraceEqn_oversetEqn_sizeEqn_textEqn_underbraceEqn_undersetEqn_vspacegaussianEliminationgetBodygetLatexgetWrappergetYmultGinvGramSchmidtgsorthhspaceinvinverseInverseis_orthogonal_matrixis_square_matrixis_symmetric_matrixJlatexMatrixlenLUmatdiffmatmultmatpowermatrix2latexmatsumminorMoorePenrosempowerNcolnewlineNrowoverbraceoversetpartitionplotEqnplotEqn3dpointOnLinepowerMethodprintMatEqnprintMatrixProjQRRrefregvec3drowaddrowCofactorsrowMinorsrowmultRownames<-rowswapshowEigshowEqnsizeSolveSVDsvdDemoswpsymMattrunderbraceundersetvandermodevecvectorsvectors3dvspacexprod

Dependencies:abindbackportsbase64encbootbroombslibcachemcarcarDataclicolorspacecowplotcpp11DerivdigestdoBydplyrevaluatefarverfastmapfontawesomeforecastFormulafracdifffsgenericsggplot2gluegtablehighrhtmltoolshtmlwidgetsisobandjquerylibjsonliteknitrlabelinglatticelifecyclelme4lmtestmagrittrMASSMatrixMatrixModelsmemoisemgcvmicrobenchmarkmimeminqamodelrnlmenloptrnnetnumDerivpbkrtestpillarpkgconfigpurrrquantregR6rappdirsrbibutilsRColorBrewerRcppRcppArmadilloRcppEigenRdpackreformulasrglrlangrmarkdownrstudioapiS7sassscalesSparseMstringistringrsurvivaltibbletidyrtidyselecttimeDatetinytexurcautf8vctrsviridisLitewithrxfunxtableyamlzoo

LaTeX Equations with latexMatrix, Eqn and matrix2latex
Using latexMatrix() and Eqn() | The SVD | Systems of equations | aligned environment | Decorators | Computing with "latexMatrix" objects | Matrix products and transpose | Determinants & inverse | Linear hypotheses | Partitioned matrices, indexing & binding | Kronecker products | matrix2latex | showEqn | References
Rendered fromlatex-equations.Rmdusingknitr::rmarkdown

Last update: 2024-11-27
Started: 2024-08-07

Properties of determinants
Create a 2 x 2 matrix | 1. Interchange two rows or cols changes the sign: -> -1 * det(A) | 2. transpose -> det (A) unchanged | 3. multiply row * k -> k * det(A) | 4. multiply matrix * k -> k^2 * det(A) | 5. det (A B) -> det(A) * det(B) | 6. proportional rows or columns -> det() == 0 | 7. Add multiple of one row to another -> det unchanged | 8. Geometric interpretation
Rendered froma1-det-ex1.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Gram-Schmidt Orthogonalization and Regression
Setup | Orthogonalization by projections | Relationship to QR factorization | Regression with X and Z
Rendered fromaA-gramreg.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Vector Spaces of Least Squares and Linear Equations
Data space | Linear equation ($\beta$) space | Observation space | References
Rendered fromaB-data-beta.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Evaluation of determinants
1. Calculate det() by cofactor expansion | Find cofactors of row 1 elements | det() = product of row with cofactors | 2. Finding det() by Gaussian elimination (pivoting) | Repeat, reducing new row, col 1 to 0 | Repeat once more. d = det(M)
Rendered froma2-det-ex2.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Inverse of a matrix
Load the matlib package | Create a 3 x 3 matrix | Basic properties | 1. det(A) != 0, so inverse exists | 2. Definition of the inverse: $A^{-1} A = A A^{-1} = I$ or AI * A = diag(nrow(A)) | 3. Inverse is reflexive: inv(inv(A)) = A | 4. inv(A) is symmetric if and only if A is symmetric | More properties of matrix inverse | 1. inverse of diagonal matrix = diag( 1/ diagonal) | 2. Inverse of an inverse: inv(inv(A)) = A | 3. inverse of a transpose: inv(t(A)) = t(inv(A)) | 4. inverse of a scalar * matrix: inv( k*A ) = (1/k) * inv(A) | 5. inverse of a matrix product: inv(A * B) = inv(B) %*% inv(A) | 6. $\det (A^{-1}) = 1 / \det(A) = [\det(A)]^{-1}$ | Geometric interpretations
Rendered froma3-inv-ex1.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Matrix inversion by elementary row operations
Load the matlib package | Create a 3 x 3 matrix | Join an identity matrix to A | Apply elementary row operations to reduce A to an identity matrix. | 1. Using R arithmetic | 2. Do the same, using matlib functions rowadd(), rowmult() and rowswap() | 3. Using echelon()
Rendered froma4-inv-ex2.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Generalized inverse
Properties of generalized inverse (Moore-Penrose inverse) | Rectangular matrices
Rendered froma5-ginv.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Linear transformations and matrix inverse in 3D
The unit cube | Define some useful functions | Show $\mathbf{I}$ and $\mathbf{A}$ all together in one figure | Same, but using separate figures, shown side by side | $A$ and $A^{-1}$ | Animate
Rendered froma6-inv-3d.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Eigenvalues and Eigenvectors: Properties
Setup | Properties of eigenvalues and eigenvectors
Rendered froma7-eigen-ex1.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Eigenvalues: Spectral Decomposition
Setup | Matrix factorization | Spectral decomposition | Further properties
Rendered froma8-eigen-ex2.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Solving Linear Equations
Conditions for a solution | Equations in two unknowns | Two consistent equations | Three consistent equations | Three inconsistent equations | Equations in three unknowns
Rendered froma9-linear-equations.Rmdusingknitr::rmarkdown

Last update: 2024-10-05
Started: 2024-10-05

Readme and manuals

Help Manual

Help pageTopics
matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics.matlib-package matlib _PACKAGE
Calculate the Adjoint of a matrixadjoint
Angle between two vectorsangle
Draw an arc showing the angle between vectorsarc
Draw 3D arrowsarrows3d
Build/Get transformation matricesas.matrix.trace buildTmat print.trace
Cholesky Square Root of a Matrixcholesky
Draw circles on an existing plot.circle
Draw a horizontal circlecircle3d
Class Data Setclass
Cofactor of A[i,j]cofactor
Data on Coffee, Stress and Heart Damagecoffee
Draw a 3D conecone3d
Draw a corner showing the angle between two vectorscorner
Determinant of a Square MatrixDet
Echelon Form of a Matrixechelon
Eigen Decomposition of a Square Symmetric MatrixEigen
Create a LaTeX Equation WrapperEqn ref
Helpers to Compose Equations with EqnEqn_helpers Eqn_hspace Eqn_newline Eqn_overbrace Eqn_overset Eqn_size Eqn_text Eqn_underbrace Eqn_underset Eqn_vspace hspace newline overbrace overset size underbrace underset vspace
Gaussian EliminationgaussianElimination print.enhancedMatrix
Correct for aspect and coordinate ratiogetYmult
Generalized Inverse of a MatrixGinv
Gram-Schmidt Orthogonalization of a MatrixGramSchmidt
Gram-Schmidt Orthogonalization of a Matrixgsorth
Inverse of a Matrixinv Inverse
Create a vector, matrix or array of constantsJ
Create and Manipulate LaTeX Representations of Matricesas.double.latexMatrix cbind.latexMatrix Colnames<- Colnames<-.latexMatrix Dim Dim.latexMatrix dimnames.latexMatrix Dimnames<- Dimnames<-.latexMatrix getBody getBody.latexMatrix getLatex getLatex.latexMatrix getWrapper getWrapper.latexMatrix is.numeric.latexMatrix latexMatrix Ncol Ncol.latexMatrix Nrow Nrow.latexMatrix partition partition.latexMatrix print.latexMatrix rbind.latexMatrix Rownames<- Rownames<-.latexMatrix [.latexMatrix
Various Functions and Operators for '"latexMatrix"' Objects%*%.latexMatrix %X% *.latexMatrix +.latexMatrix -.latexMatrix determinant.latexMatrix Dot inverse inverse.latexMatrix kronecker,latexMatrix,latexMatrix-method latexMatrixOperations matdiff matdiff.latexMatrix matmult matmult.latexMatrix matpower matpower.latexMatrix matsum matsum.latexMatrix solve.latexMatrix t.latexMatrix ^.latexMatrix
Length of a Vector or Column Lengths of a Matrixlen
LU DecompositionLU
(Deprecated) Convert matrix to LaTeX equationmatrix2latex
Minor of A[i,j]minor
Moore-Penrose inverse of a matrixMoorePenrose
Matrix Powermpower
Plot method for regvec3d objectsplot.regvec3d print.regvec3d summary.regvec3d
Plot Linear EquationsplotEqn
Plot Linear Equations in 3DplotEqn3d
Position of a point along a linepointOnLine
Power Method for EigenvectorspowerMethod
Print Matrices or Matrix Operations Side by SideprintMatEqn
(Deprecated) Print a matrix, allowing fractions or LaTeX outputprintMatrix
Projection of Vector y on columns of XProj
QR Decomposition by Graham-Schmidt OrthonormalizationQR
Rank of a MatrixR
Vector space representation of a two-variable regression modelregvec3d regvec3d.default regvec3d.formula
Elementary Row Operationsrowadd
Row Cofactors of A[i,]rowCofactors
Row Minors of A[i,]rowMinors
Multiply Rows by Constantsrowmult
Interchange two rows of a matrixrowswap
Show the eigenvectors associated with a covariance matrixshowEig
Show Matrices (A, b) as Linear EquationsshowEqn
Solve and Display Solutions for Systems of Linear Simultaneous EquationsSolve
Singular Value Decomposition of a MatrixSVD
Demonstrate the SVD for a 3 x 3 matrixsvdDemo
The Matrix Sweep Operatorswp
Create a Symmetric Matrix from a VectorsymMat
Therapy Datatherapy
Trace of a Matrixtr
Vandermode Matrixvandermode
Vectorize a Matrixvec
Draw geometric vectors in 2Dvectors
Draw 3D vectorsvectors3d
Workers Dataworkers
Generalized Vector Cross Productxprod