useful math

%% is modulo division (i.e., we just keep track of the remainder)

> 1:9 %% 2  # after dividing by 2, what is left?
[1] 1 0 1 0 1 0 1 0 1
> 1:9 %% 3  # after dividing by 3, what is left?
[1] 1 2 0 1 2 0 1 2 0
> 1:9 %% 4 
[1] 1 2 3 0 1 2 3 0 1

%/% is integer division (i.e., we just ignore the remainder)

> 1:9 %/% 2
[1] 0 1 1 2 2 3 3 4 4  # how many times can 2 go into each number?
> 1:9 %/% 3
[1] 0 0 1 1 1 2 2 2 3 
> 1:9 %/% 4
[1] 0 0 0 1 1 1 1 2 2

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Use matrix(data, nrow, ncol, byrow) to create plot-able, transformable matrices. data is the values in the matrix. nrow is the number of rows, and ncol the number of columns. byrow specifies how to fill the matrix (=TRUE for by row, =FALSE for by column). byrow defaults to FALSE.

Examples (from http://www.ats.ucla.edu/stat/R/library/matrix_alg.htm):

>seq1 <- seq(1:6)
>mat1 <- matrix(seq1, 2)
>mat1
     [,1] [,2] [,3] 
[1,]    1    3    5
[2,]    2    4    6

#filling the matrix by rows
>mat2 <- matrix(seq1, 2, byrow = T)
>mat2
     [,1] [,2] [,3] 
[1,]    1    2    3
[2,]    4    5    6

>mat3 <- matrix(seq1, ncol = 2)
>mat3
     [,1] [,2] 
[1,]    1    4
[2,]    2    5
[3,]    3    6

#creating the same matrix using both dimension arguments
#by using them in order we do not have to name them

>mat4 <- matrix(seq1, 3, 2)
>mat4
     [,1] [,2] 
[1,]    1    4
[2,]    2    5
[3,]    3    6

See http://www.statmethods.net/advstats/matrix.html for a list of matrix functions.