LaTeX Equations with latexMatrix, Eqn and matrix2latex
Phil Chalmers, John Fox, Michael Friendly
2024-10-05
Source:vignettes/latex-equations.Rmd
latex-equations.Rmd
LaTeX is the de facto standard for communication and publication in
scientific documents and it is very easy to typeset mathematical
expressions like Pythagoras’ theorem,
(using a^2 + b^2 = c^2
) once you learn the notation. With a
bit of practice, the PDF of the normal distribution can be written
as
f(x) = \frac{1}{\sigma\sqrt{2\pi}}
\exp\left[ -\left(\frac{x-\mu}{2\sigma}\right)^{\!2}\,\right]
which renders as
Writing equations with arrays, matrices and vectors is somewhat more challenging. Many people rely on interactive LaTeX editors like Overleaf, MathType, or online versions like Lagrida LaTeX Equation Editor that provide a menu-driven interface with fill-in templates for matrices.
There are already some tools available in R for producing LaTeX output:
- tables (e.g,
xtable::xtable()
,tables::toLatex()
), - R objects (
Hmisc::latex()
), - statistical models (
equatiomatic::extract_eq()
), -
knitr::knit_print()
can be used to define methods for printing objects of class"matrix"
. - The
mathpix
package can take an image of a an equation or formula and produce the LaTeX code which should generate that image. - The
texPreview
package compiles snippets of LaTeX directly into images from the R console to view in the RStudio viewer pane, Shiny apps and Rmarkdown documents.
See Tools for making latex tables in R for a more comprehensive list
The matlib
package extends these, providing a collection
of functions that simplify using LaTeX notation for matrices, vectors
and equations in documentation and in writing:
-
latexMatrix()
: Constructs the LaTeX code for a symbolic matrix, whose elements are a symbol, with row and column subscripts.latexMatrix()
also supports matrices with numeric elements, and the objects it produces may be used in various kinds of matrix computations, both symbolic and numeric. -
Eqn()
: A wrapper to produce LaTeX expressions or equations that can be used directly in.Rmd
or.qmd
documents to compile to equations. It also provides for direct preview of the resulting equation. -
showEqn()
: Shows what matrices look like as the system of linear equations, , but written out as a set of equations.
When used directly in R, these functions produce their output to the
console (using cat()
). In a .Rmd
or
.qmd
document, use the chunk options:
results='asis', echo=FALSE
so that knitr
just
outputs the text of the equations to the document. The rendering of the
equations is mediated by pandoc
for standard
Rmarkdown or Quarto documents.
Note: There are several different engines for
rendering mathematics in HTML documents for the Web: mathml
,
katex
, and mathjax
and others, all
of which can be made to work with pandoc
. The features we
describe below work in standard Rmarkdown or Quarto documents. However,
some more advanced features (horizontal and vertical lines for
partitioned matrices) require katex
to work with pkgdown
. Equation
numbers and cross-references to them still do not work in
pkgdown
. See the discussion in this pkgdown
issue. Rendering of matrix equations doesn’t seem to work at all in
the friendly.r-universe.dev
version of this vignette.
Using latexMatrix()
and Eqn()
latexMatrix()
constructs the LaTeX code for a symbolic
matrix, whose elements are a symbol, with row and column subscripts. For
example, by default (with no arguments) it produces the expression for
an
matrix
whose elements are
in a LaTeX \begin{pmatrix} ... \end{pmatrix}
environment.
The LaTeX code generated looks like this:
\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1m} \\
x_{21} & x_{22} & \cdots & x_{2m} \\
\vdots & \vdots & & \vdots \\
x_{n1} & x_{n2} & \cdots & x_{nm} \\
\end{pmatrix}
The code above appears in the console. To render this as a matrix in
a document, this must be wrapped in a display math environment,
typically specified as $$ ... $$
or \[ ... \]
.
This is provided by Eqn()
and used in a code chunk with the
results = 'asis'
option, giving the rendered
expression.
latexMatrix() |> Eqn()
For chunk output in a document, you will get a LaTeX error, “missing
$ inserted” if you forget to use Eqn()
or otherwise fail to
make the LaTeX appear inside a math environment.
Some other examples:
- A
identity matrix with square brackets, specified as an equation with a
left-hand side
.
The first argument to
latexMatrix()
can be any numeric matrix. Thematrix="bmatrix"
argument here specifies square brackets around the matrix.
Eqn("\\mathbf{I}_3 =", latexMatrix(diag(3), matrix="bmatrix"))
- A row or column vector; the first argument to
latexMatrix()
must be a matrix, so wrap an R vector inmatrix()
, supplyingnrow=1
(orncol = 1
):
latexMatrix(matrix(LETTERS[1:4], nrow=1), matrix="Bmatrix") |> Eqn()
latexMatrix(matrix(letters[1:3], ncol=1), matrix = "vmatrix") |> Eqn()
The above examples illustrate, some styles of matrix delimiters using
the matrix
argument.
A wide variety of options are available for the matrix element symbols, fonts, subscripts and decorations:
- The typical element can use any LaTeX math font, e.g.,
\\mathbb{}, \mathcal{}, ...
; - the row/column subscripts can start at 0 or 1;
- they can be separated by a comma, and
- one can apply an exponent () or transpose symbol ( or )
latexMatrix("\\mathbb{q}", 3, 3,
matrix = "bmatrix",
zero.based = c(TRUE, FALSE),
comma=TRUE,
exponent="-1") |>
Eqn()
The SVD
As a more complicated example, here we write out the LaTeX equation
for the singular
value decomposition (SVD) of a general
matrix
using Eqn()
and latexMatrix()
. In Rmd markup,
Eqn()
can be given an equation label
(using the label
argument), which will both label and
number the equations.
Two calls to Eqn()
produce separate equations in the
output below. Both of these equations are numbered. (Eqn()
uses the LaTeX equation
environment,
\begin{equation} ... \end{equation}
, or
equation*
if the equation does not include a
label
). The two calls to Eqn()
are rendered as
separate equations, center aligned.
Eqn("\\mathbf{X} = \\mathbf{U} \\mathbf{\\Lambda} \\mathbf{V}^\\top", label='eq:svd')
Eqn("\\mathbf{X} =",
latexMatrix("u", "n", "k"),
latexMatrix("\\lambda", "k", "k", diag=TRUE),
latexMatrix("v", "k", "p", transpose = TRUE), label='eq:svdmats')
This produces the two numbered equations:1
The matrix names in Equation @ref(eq:svd) are printed in a
boldface math font (\mathbf{}
), typically
used for matrices and vectors. Note that when using LaTeX code in R
expressions each backslash (\
) must be doubled
(\\
) in R because \
is the escape
character.
Note that the first equation can be referenced because it was
labeled: “As seen in Equation @ref(eq:svd) ”. References to equations
can entered in text using an inline call to ref()
, e.g,
`r ref("eq:svd")`
(In Quarto, equation labels must be of
the form #eq-label
and equation references are of the form
@eq-label
)
Systems of equations
As another example, the chunk below shows a system of equations written out using symbolic matrices.
Eqn(latexMatrix("a", nrow = "m", ncol="n", matrix="bmatrix"),
latexMatrix("x", nrow = "n", ncol=1),
Eqn_hspace(mid='='),
latexMatrix("b", nrow = "m", ncol=1))
Extra symmetric white space is added via Eqn_hspace()
,
which can also be used for standard spacing such as \quad
(default size), \,
, '1cm'
for
\hspace{}
, etc.
Section showEqn describes another way to display systems of equations.
aligned
environment
You can also align separate equations relative to some symbol like an
=
sign to show separate steps of re-expression, using the
option Eqn(..., align=TRUE)
. Alignment points are marked by
&
in LaTeX.
Show the singular value decomposition again, but now as two separate
equations aligned after the =
sign. Note the locations of
the &
operator for alignment, specified as the
left-hand side (lhs
) of the second equation.
Eqn("\\mathbf{X} & = \\mathbf{U} \\mathbf{\\Lambda} \\mathbf{V}^\\top",
Eqn_newline(),
' & =',
latexMatrix("u", "n", "k"),
latexMatrix("\\lambda", "k", "k", diag=TRUE),
latexMatrix("v", "k", "p", transpose = TRUE),
align=TRUE)
Note that in this example, there are three calls to
latexMatrix()
, wrapped inside Eqn()
.
Eqn_newline()
emits a newline (\\
) between
equations.
Computing with "latexMatrix"
objects
Objects returned by latexMatrix()
that have
definite (i.e., numeric) dimensions— for example, a
3-by-2 matrix as opposed to an “n”-by-“m” matrix—may be employed in a
variety of standard symbolic and numeric matrix computations. They
provide some reasonable means to compose meaningful matrix equations in
LaTeX far easier than doing this manually, matrix by matrix.
These computations include:
- the R arithmetic operators
+
(matrix addition),-
(matrix subtraction and negation),*
(product of a scalar and a matrix), -
^
(raise to a power), and -
%*%
(matrix multiplication), and the functionst()
(transpose),determinant()
, andsolve()
(matrix inverse), -
%O%
(kronecker product), - Selecting sub-matrices using indexing
X[rows, cols]
and binding rows/columns withrbind()
,cbind()
There are also function equivalents of the operators that are more
flexible via optional arguments. For example, using the operator
A %*% B
multiplies the two matrices A
and
B
, returning a symbolic result. The corresponding function
matmult()
multiplies two or more matrices, and can
simplify the result (with simplify = TRUE
, default) and/or
produce the numeric representation of the product (with
as.numeric = TRUE
, default).
With the exception of determinant()
, which (because it
is a scalar quantity) returns a character string with a LaTeX expression
for the determinant, these operators and functions return
"latexMatrix"
objects, which can be printed, typeset, or
used in further computations. Additionally, in many instances a
"latexMatrix"
object can be coerced to a numeric matrix by
as.double()
. We illustrate
these computations in this section.
Consider, first, basic matrix arithmetic. Define some matrices:
A
and B
are numeric, but C
and
D
are symbolic, with elements
and
(A <- latexMatrix(matrix(c(1, -3, 0, 1), 2, 2)))
## \begin{pmatrix}
## 1 & 0 \\
## -3 & 1 \\
## \end{pmatrix}
(B <- latexMatrix(matrix(c(5, 3, -1, 4), 2, 2)))
## \begin{pmatrix}
## 5 & -1 \\
## 3 & 4 \\
## \end{pmatrix}
(C <- latexMatrix(symbol="c", 2, 3))
## \begin{pmatrix}
## c_{11} & c_{12} & c_{13} \\
## c_{21} & c_{22} & c_{23} \\
## \end{pmatrix}
(D <- latexMatrix(symbol="d", 2, 3))
## \begin{pmatrix}
## d_{11} & d_{12} & d_{13} \\
## d_{21} & d_{22} & d_{23} \\
## \end{pmatrix}
The usual arithmetic operations work for these
"latexMatrix"
objects, and return LaTeX representations of
the result:
A + B
## \begin{pmatrix}
## 6 & -1 \\
## 0 & 5 \\
## \end{pmatrix}
Some other examples:
A - B
## \begin{pmatrix}
## -4 & 1 \\
## -6 & -3 \\
## \end{pmatrix}
-A # unary minus
## \begin{pmatrix}
## -1 & 0 \\
## 3 & -1 \\
## \end{pmatrix}
2*A # scalar multiplication
## \begin{pmatrix}
## 2 \cdot 1 & 2 \cdot 0 \\
## 2 \cdot (-3) & 2 \cdot 1 \\
## \end{pmatrix}
C + D # sum of symbolics
## \begin{pmatrix}
## c_{11} + d_{11} & c_{12} + d_{12} & c_{13} + d_{13} \\
## c_{21} + d_{21} & c_{22} + d_{22} & c_{23} + d_{23} \\
## \end{pmatrix}
"\\pi" * C # everything should be multiplied by pi
## \begin{pmatrix}
## \pi \cdot c_{11} & \pi \cdot c_{12} & \pi \cdot c_{13} \\
## \pi \cdot c_{21} & \pi \cdot c_{22} & \pi \cdot c_{23} \\
## \end{pmatrix}
Typesetting the last result produces:
Some of these operations produce numeric results and so can be coerced to numeric matrices; for example:
as.numeric(A + B)
## [,1] [,2]
## [1,] 6 -1
## [2,] 0 5
Using these tools, it is easy to typeset complete matrix equations,
giving multiple arguments to Eqn()
:
Eqn("\\mathbf{A} + \\mathbf{B} =", A, " + ", B, " = ", A + B)
If the elements of a matrix are valid R variable names, then it is also possible to give these elements numeric values, as in
(M <- latexMatrix(matrix(letters[1:9], 3, 3)))
## \begin{pmatrix}
## a & d & g \\
## b & e & h \\
## c & f & i \\
## \end{pmatrix}
## [,1] [,2] [,3]
## [1,] -2 8 0
## [2,] 0 -14 -8
## [3,] 4 2 -12
Matrix products and transpose
The product of two matrices is given by %*%
for
"latexMatrix"
objects. When the arguments are both numeric,
the numeric result is evaluated and presented in LaTeX form.
A %*% B
But the result is symbolic if either argument is symbolic:
A %*% latexMatrix("b", 2, 2)
The LaTeX symbol for multiplication is a centered dot,
\\cdot
(),
by default. This can be changed by changing
options(latexMultSymbol)
, e.g, to use the
symbol instead, use:
options(latexMultSymbol = "\\times")
The transpose, t()
of "latexMatrix"
objects
is similarly straightforward. This directly transposes the matrix, as
opposed to superscript notation,
or
which is implicit.
D
## \begin{pmatrix}
## d_{11} & d_{12} & d_{13} \\
## d_{21} & d_{22} & d_{23} \\
## \end{pmatrix}
t(D)
## \begin{pmatrix}
## d_{11} & d_{21} \\
## d_{12} & d_{22} \\
## d_{13} & d_{23} \\
## \end{pmatrix}
## \begin{pmatrix}
## a \cdot d_{11} + d \cdot d_{12} + g \cdot d_{13} & a \cdot d_{21} + d \cdot d_{22} + g \cdot d_{23} \\
## b \cdot d_{11} + e \cdot d_{12} + h \cdot d_{13} & b \cdot d_{21} + e \cdot d_{22} + h \cdot d_{23} \\
## c \cdot d_{11} + f \cdot d_{12} + i \cdot d_{13} & c \cdot d_{21} + f \cdot d_{22} + i \cdot d_{23} \\
## \end{pmatrix}
The matrix product in the previous example typesets as
Determinants & inverse
The determinant is computed recursively by finding the cofactors of the first row of the matrix, i.e., where the cofactors involve the determinants of the minors . (See the vignette Evaluation of determinants for explanation.)
The method is applicable to a matrix of any order, although beyond an order-3 matrix, the resulting expression gets very long. A couple of examples:
A
## \begin{pmatrix}
## 1 & 0 \\
## -3 & 1 \\
## \end{pmatrix}
determinant(A)
## [1] "1 \\cdot 1 - 0 \\cdot (-3)"
M
## \begin{pmatrix}
## a & d & g \\
## b & e & h \\
## c & f & i \\
## \end{pmatrix}
determinant(M)
## [1] "a \\cdot (e \\cdot i - h \\cdot f) - d \\cdot (b \\cdot i - h \\cdot c) + g \\cdot (b \\cdot f - e \\cdot c)"
The determinant of a matrix is a single number.
determinant()
returns the expression that computes it in
LaTeX notation, using \\cdot
to represent
for multiplication.
Typesetting the output from the last command produces
The inverse of a square matrix is computed from its determinant and adjoint matrix; for example:
solve(A)
## \begin{pmatrix}
## 1 & 0 \\
## 3 & 1 \\
## \end{pmatrix}
Specifying the argument simplify = TRUE
to
solve()
puts the inverse determinant before the adjoint
matrix and returns a latex expression rather than a
"latexMatrix"
object; for example:
solve(M, simplify=TRUE)
## [1] "\\frac{1}{a \\cdot (e \\cdot i - h \\cdot f) - d \\cdot (b \\cdot i - h \\cdot c) + g \\cdot (b \\cdot f - e \\cdot c)} \n\\begin{pmatrix} \ne \\cdot i - h \\cdot f & -(d \\cdot i - g \\cdot f) & d \\cdot h - g \\cdot e \\\\ \n-(b \\cdot i - h \\cdot c) & a \\cdot i - g \\cdot c & -(a \\cdot h - g \\cdot b) \\\\ \nb \\cdot f - e \\cdot c & -(a \\cdot f - d \\cdot c) & a \\cdot e - d \\cdot b \\\\ \n\\end{pmatrix}\n"
which typesets as
We can also supply values for the elements of the matrix to obtain a numeric inverse:
## [,1] [,2] [,3]
## [1,] 23/39 4/13 -8/39
## [2,] -4/39 1/13 -2/39
## [3,] 7/39 3/26 7/78
## [1] 78
Linear hypotheses
As an example of the more general use of these functions, consider the general linear hypothesis used to test hypotheses and contrasts in linear models. We consider a multivariate regression model with regressors (including the constant for the intercept) and responses, .
Suppose we want to test the hypothesis that a subset of rows (predictors) and/or columns (responses) simultaneously have null effects. This can be expressed in the general linear test, where is a full rank hypothesis matrix of constants, that selects subsets or linear combinations (contrasts) of the coefficients in to be tested in a degree-of-freedom hypothesis.
For example, for a multivariate regression model with three responses
and three predictors
,
the coefficients
are given by the following latexMatrix()
expression, where
several arguments are used to: (a) start row indices at zero
(zero.based
); (b) make the column indices a subscript of
(prefix.col
); (c) insert a comma between row/column
subscripts.
(B <- latexMatrix('\\beta', ncol = 3, nrow=4,
comma=TRUE, prefix.col = 'y_',
zero.based=c(TRUE, FALSE)))
We can test the hypothesis that neither nor contribute at all to the predicting the s in terms of the hypothesis that the coefficients for the corresponding rows of are zero. To do this, we specify a 2-row matrix that simply selects those rows:
(C <- latexMatrix(matrix(c(0, 1, 0, 0,
0, 0, 1, 0), nrow=2, byrow=TRUE),
matrix = "bmatrix"))
Then, the hypothesis to be tested can be expressed as follows, using
Eqn()
to wrap a set of LaTeX expressions and calls to
matlib
functions.
B0 <- latexMatrix('\\beta', ncol = 3, nrow=2, comma=TRUE, prefix.col = 'y_')
Eqn("\\mathcal{H}_0 : \\mathbf{C} \\mathbf{B} & = ",
C, B,
Eqn_newline(),
'& =',
B0,
"= \\mathbf{0}_{(2 \\times 3)}",
align=TRUE)
In this example, note that the R objects C
,
B
and B0
are the results of
latexMatrix()
calls, which are character strings containing
LaTeX expressions.
Partitioned matrices, indexing & binding
Matrix notation sometimes portrays matrices whose elements are themselves matrices and vectors (rather than scalars) in order to show a higher-level structure. Such matrices, called partitioned or block matrices have similar arithmetic and algebraic properties to those of ordinary matrices.
For example, the code below represents a matrix , which is partitioned in blocks, which are labeled .
M <- latexMatrix("m", 4, 4)
Mpart <- latexMatrix('\\mathbf{M}', nrow = 2, ncol = 2, comma = TRUE)
Eqn("\\mathbf{M} =", Mpart,
" =", M)
##
## \begin{equation*}
## \mathbf{M} =\begin{pmatrix}
## \mathbf{M}_{1,1} & \mathbf{M}_{1,2} \\
## \mathbf{M}_{2,1} & \mathbf{M}_{2,2} \\
## \end{pmatrix}
## =\begin{pmatrix}
## m_{11} & m_{12} & m_{13} & m_{14} \\
## m_{21} & m_{22} & m_{23} & m_{24} \\
## m_{31} & m_{32} & m_{33} & m_{34} \\
## m_{41} & m_{42} & m_{43} & m_{44} \\
## \end{pmatrix}
## \end{equation*}
This typesets as:
Just as rows and columns can be selected using
X[rows, cols]
indexing for ordinary matrices, the same
operator can be used for LaTeX matrices, e.g.,
M[rows, cols]
. The following extracts 4 the sub-matrices of
M
:
M11 <- M[1:2, 1:2] |> print()
## \begin{pmatrix}
## m_{11} & m_{12} \\
## m_{21} & m_{22} \\
## \end{pmatrix}
M12 <- M[1:2, 3:4]
M21 <- M[3:4, 1:2]
M22 <- M[3:4, 3:4]
The operations of joining matrices by rows, with
rbind()
, and by columns, with cbind()
are also
defined for "latexMatrices"
. This code puts the 4 pieces of
back together:
## \begin{pmatrix}
## m_{11} & m_{12} & m_{13} & m_{14} \\
## m_{21} & m_{22} & m_{23} & m_{24} \\
## m_{31} & m_{32} & m_{33} & m_{34} \\
## m_{41} & m_{42} & m_{43} & m_{44} \\
## \end{pmatrix}
And, of course you can also format the sub-matrices together using
Eqn()
:
Eqn(M11, M12,
Eqn_newline(),
M21, M22,
align = TRUE)
Finally, the partition()
function alters the print
representation of a matrix using horizontal and vertical lines
separating the sub-matrices. It does this by re-wrapping the matrix in a
LaTeX \begin{array} ... \end{array}
environment, using
|
in {c c | c c}
for the vertical lines and
\hline
for horizontal lines. This may be the simplest way
to portray partitioned matrices in writing.
partition(M, rows=2, columns=2)
Note that partition()
can show more than one horizontal
and vertical partition lines (or no line at all):
Using this notation, we can illustrate matrix arithmetic with partitioned matrices. For example, assuming the partitions of matrices and are of the same size, their sum is just the sum of corresponding sub-matrices:
C <- latexMatrix("\\mathbf{C}", 2, 2)
D <- latexMatrix("\\mathbf{D}", 2, 2)
Eqn("\\mathbf{C} + \\mathbf{D} =",
C, "+", D, "=",
C + D)
Kronecker products
The Kronecker product of two matrices, is the block matrix consisting of each element multiplied by . This has many uses in statistics, among these the nice result (Bock 1975; Sunwoo 1996) that the design matrix in the linear ANOVA model for factors A, B, C, … can be generated as the Kronecker product of their contrast matrices , each preceded by the unit vector .
This is implemented in the %O%
operator and the
kronecker()
function in the package. For example,
A <- matrix(1:4, nrow = 2) |>
latexMatrix() |> print()
B <- matrix(5:8, nrow = 2) |>
latexMatrix() |> print()
You can also use Eqn()
to illustrate the definition of
the Kronecker product more explicitly. In the following,
KAB
is the product in symbolic form;
as.double()
is used to evaluate the result numerically.
Bmat <- latexMatrix('\\mathbf{B}', ncol=1, nrow=1)
KABmat <- kronecker(A, Bmat)
KAB <- kronecker(A, B)
Eqn("\\mathbf{A} \\otimes \\mathbf{B} = &",
KABmat,
Eqn_newline(space = '1.5ex'), "= & ",
KAB |> partition(rows = 2, columns = 2),
Eqn_newline(space = '1.5ex'), "= & ",
latexMatrix(as.double(KAB)) |> partition(rows = 2, columns = 2),
align = TRUE)
$$\begin{align*} \mathbf{A} \otimes \mathbf{B} = &\begin{pmatrix} 1 \cdot \mathbf{B} & 3 \cdot \mathbf{B} \\ 2 \cdot \mathbf{B} & 4 \cdot \mathbf{B} \\ \end{pmatrix} \\[1.5ex] = & \begin{pmatrix} \begin{array}{c c | c c} 1 \cdot 5 & 1 \cdot 7 & 3 \cdot 5 & 3 \cdot 7\\ 1 \cdot 6 & 1 \cdot 8 & 3 \cdot 6 & 3 \cdot 8\\ \hline 2 \cdot 5 & 2 \cdot 7 & 4 \cdot 5 & 4 \cdot 7\\ 2 \cdot 6 & 2 \cdot 8 & 4 \cdot 6 & 4 \cdot 8\\ \end{array} \end{pmatrix} \\[1.5ex] = & \begin{pmatrix} \begin{array}{c c | c c} 5 & 7 & 15 & 21\\ 6 & 8 & 18 & 24\\ \hline 10 & 14 & 20 & 28\\ 12 & 16 & 24 & 32\\ \end{array} \end{pmatrix}\end{align*}$$
matrix2latex
The matrix2latex()
function can also generate symbolic
equations from numeric or character matrices. For numeric matrices, it
can round the values or show results as fractions.
A <- matrix(1:12, nrow=3, ncol=4, byrow = TRUE) / 6
matrix2latex(A, fractions = TRUE, brackets = "b") |> Eqn()
Say we want to show the matrix involved in the system of equations . Create these as a character matrix and vector:
## [,1] [,2] [,3]
## [1,] "a_1" "a_2" "a_3"
## [2,] "a_4" "a_5" "a_6"
## [3,] "a_7" "a_8" "a_9"
## [1] "\\beta_1" "\\beta_2" "\\beta_3"
Then use matrix2latex()
on cbind(A,b)
and
pipe the result of matrix2latex()
to
Eqn()
:
matrix2latex(cbind(A,b)) |> Eqn()
All the R tricks for creating and modifying matrices can be used in this way.
showEqn
showEqn()
is designed to show a system of linear
equations,
,
but written out as a set of equations individually. With the option
latex = TRUE
it writes these out in LaTeX form.
Here, we create a character matrix containing the elements of a
matrix A
, whose elements are of the form
a_{ij}
and two character vectors, b_i
and
x_i
.
## [,1] [,2] [,3]
## [1,] "a_{11}" "a_{12}" "a_{13}"
## [2,] "a_{21}" "a_{22}" "a_{23}"
## [3,] "a_{31}" "a_{32}" "a_{33}"
showEqn(..., latex = TRUE)
produces the three equations
in a single \begin{array} ... \begin{array}
environment.
showEqn(A, b, vars = x, latex=TRUE)
If this line was run in an R console, it would produce:
\begin{array}{lllllll}
a_{11} \cdot x_1 &+& a_{12} \cdot x_2 &+& a_{13} \cdot x_3 &=& b_1 \\
a_{21} \cdot x_1 &+& a_{22} \cdot x_2 &+& a_{23} \cdot x_3 &=& b_2 \\
a_{31} \cdot x_1 &+& a_{32} \cdot x_2 &+& a_{33} \cdot x_3 &=& b_3 \\
\end{array}
Evaluating the above code in an unnumbered LaTeX math environment via
Eqn()
gives the desired result: