How can I create a correlation matrix in R?

You could use 'corrplot' package.

d <- data.frame(x1=rnorm(10),
                 x2=rnorm(10),
                 x3=rnorm(10))
M <- cor(d) # get correlations

library('corrplot') #package corrplot
corrplot(M, method = "circle") #plot matrix

More information here: http://cran.r-project.org/web/packages/corrplot/vignettes/corrplot-intro.html

The cor function will use the columns of the matrix in the calculation of correlation. So, the number of rows must be the same between your matrix x and matrix y. Ex.:

set.seed(1)
x <- matrix(rnorm(20), nrow=5, ncol=4)
y <- matrix(rnorm(15), nrow=5, ncol=3)
COR <- cor(x,y)
COR
image(x=seq(dim(x)[2]), y=seq(dim(y)[2]), z=COR, xlab="x column", ylab="y column")
text(expand.grid(x=seq(dim(x)[2]), y=seq(dim(y)[2])), labels=round(c(COR),2))

Edit:

Here is an example of custom row and column labels on a correlation matrix calculated with a single matrix:

png("corplot.png", width=5, height=5, units="in", res=200)
op <- par(mar=c(6,6,1,1), ps=10)
COR <- cor(iris[,1:4])
image(x=seq(nrow(COR)), y=seq(ncol(COR)), z=cor(iris[,1:4]), axes=F, xlab="", ylab="")
text(expand.grid(x=seq(dim(COR)[1]), y=seq(dim(COR)[2])), labels=round(c(COR),2))
box()
axis(1, at=seq(nrow(COR)), labels = rownames(COR), las=2)
axis(2, at=seq(ncol(COR)), labels = colnames(COR), las=1)
par(op)
dev.off()

Have a look at qtlcharts. It allows you to create interactive correlation matrices:

library(qtlcharts)
data(iris)
iris$Species <- NULL
iplotCorr(iris, reorder=TRUE)

It's more impressive when you correlate more variables, like in the package's vignette:

There are other ways to achieve this here: (Plot correlation matrix into a graph), but I like your version with the correlations in the boxes. Is there a way to add the variable names to the x and y column instead of just those index numbers? For me, that would make this a perfect solution. Thanks!

edit: I was trying to comment on the post by [Marc in the box], but I clearly don't know what I'm doing. However, I did manage to answer this question for myself.

if d is the matrix (or the original data frame) and the column names are what you want, then the following works:

axis(1, 1:dim(d)[2], colnames(d), las=2)
axis(2, 1:dim(d)[2], colnames(d), las=2)

las=0 would flip the names back to their normal position, mine were long, so I used las=2 to make them perpendicular to the axis.

edit2: to suppress the image() function printing numbers on the grid (otherwise they overlap your variable labels), add xaxt='n', e.g.:

image(x=seq(dim(x)[2]), y=seq(dim(y)[2]), z=COR, col=rev(heat.colors(20)), xlab="x column", ylab="y column", xaxt='n')

Have a look at the datasummary_correlation (article, vignette) function of modelsummary.

Here is an example of a typical correlation table:

library(correlation)
library(modelsummary)
library(tidyverse)

fun <- function(x) {
  out <- x |>
    correlation() |>
    summary(redundant = TRUE) |>
    format(digits=2)  |>
    as.matrix()
  row.names(out) <- out[, 1]
  out <- out[, 2:ncol(out)]
  lt <- upper.tri(out)
  out[lt] <- ""
  diag(out) <- rep("1.00", nrow(out))
  return(out)
}

datasummary_correlation(
  mtcars, 
  method = fun)