Delete every second row and column from spatial point data in R - r

Question

I have converted a raster to a point matrix in R. The file has 3 columns, x (lon), y (lat) and v (pixel value) - I am now looking to delete every second column by x and every second row by y as shown in the upper left corner of the image but am at loss how to do this. The idea is to thin the data without any interpolation or resampling.
Sample data as shown can be accessed here: https://drive.google.com/file/d/1XGEPsPEyrVNLEcZy-C6ES5915kWIaqGz/view?usp=sharing

Answer 1

When asking an R question, please always include a minimal reproducible, self-contained example, that is show some code and do not rely on files that must be downloaded.
As you started out with raster data, it is probably easiest to manipulate the raster data before creating points.
With the raster package:
Example data
library(raster)
r <- raster(nrow=20, ncol=20, xmn=0, xmx=1, ymn=0, ymx=1, crs="+proj=utm +zone=1 +datum=WGS84")
values(r) <- 1:ncell(r)
p <- rasterToPoints(r)
plot(r)
points(p, cex=.5)
Solution
i <- seq(1, nrow(r), 2)
j <- seq(1, ncol(r), 2)
r[i,] <- NA
r[, j] <- NA
pp <- rasterToPoints(r)
points(pp, pch=20, cex=2)
Or with the terra package:
library(terra)
r <- rast(nrow=20, ncol=20, xmin=0, xmax=1, ymin=0, ymax=1, crs="+proj=utm +zone=1 +datum=WGS84")
values(r) <- 1:ncell(r)
p <- as.points(r)
plot(r)
points(p, cex=.5)
i <- seq(1, nrow(r), 2)
j <- seq(1, ncol(r), 2)
r[i,] <- NA
r[, j] <- NA
pp <- as.points(r)
points(pp, pch=20, cex=2)

Answer 2

Does this work? Hard to know what to manipulate without a reproducible example and desired output, but this should remove even rows and columns from your matrix.
library(dplyr)
matrix(1:100, nrow = 10) %>%
as.data.frame() %>%
filter(row_number() %% 2 != 0) %>%
select(seq(1, ncol(.), 2)) %>%
as.matrix()