> x = rbind(c(10, "[]", "[[1,2]]"), c(20, "[]", "[[1,3]]"))
> x
     [,1] [,2] [,3]     
[1,] "10" "[]" "[[1,2]]"
[2,] "20" "[]" "[[1,3]]"

> x <- matrix(c(8,1,1,4),2,2)
> x

     [,1] [,2]
[1,]    8    1
[2,]    1    4


> y <- chol(x)
> y

         [,1]      [,2]
[1,] 2.828427 0.3535534
[2,] 0.000000 1.9685020

> x <- matrix(rep(1:4),2,2)
> x

     [,1] [,2]
[1,]    1    3
[2,]    2    4


> y <- chol(x)

Error in chol.default(x) : 
  the leading minor of order 2 is not positive definite

list()

data.frame()

> library(MASS)      # load the MASS package

> painters 

              Composition Drawing Colour Expression School 

Da Udine               10       8     16          3      A 

Da Vinci               15      16      4         14      A 

Del Piombo              8      13     16          7      A 

Del Sarto              12      16      9          8      A 

Fr. Penni               0      15      8          0      A 

Guilio Romano          15      16      4         14      A 

> painters$School 

 [1] A A A A A A A A A A B B B B B B C C C C C C D D D D 

[27] D D D D D D E E E E E E E F F F F G G G G G G G H H 

[53] H H 

Levels: A B C D E F G H 

> school = painters$School      # the painter schools 
> school.freq = table(school)   # apply the table function 
> school.freq 
school 
 A  B  C  D  E  F  G  H 
10  6  6 10  7  4  7  4 
> cbind(school.freq) 
  school.freq 
A          10 
B           6 
C           6 
D          10 
E           7 
F           4 
G           7 
H           4 

> school.relfreq = school.freq / nrow(painters) 

> school.relfreq 

school 

       A        B        C        D        E        F 

0.185185 0.111111 0.111111 0.185185 0.129630 0.074074 

       G        H 

0.129630 0.074074

> barplot(school.freq)  

> colors = c("red", "yellow", "green", "violet", 

+   "orange", "blue", "pink", "cyan") 

> barplot(school.freq,         # apply the barplot function 

+   col=colors)                # set the color palette 

> pie(school.freq)      
> colors = c("red", "yellow", "green", "violet", 
+   "orange", "blue", "pink", "cyan") 
> pie(school.freq,             # apply the pie function 
+   col=colors)                # set the color palette 

> cc<-c(1,2,3,4,5,2,1,2,3,4,3,2,1,2,3,4,3,2,1,2,5,4,3,2,1)
> A<-matrix(cc,5,5)
> A
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    2    3    4    5
[2,]    2    1    2    3    4
[3,]    3    2    1    2    3
[4,]    4    3    2    1    2
[5,]    5    4    3    2    1
> b<-matrix(c(7,-1,-3,5,17),5,1)
> b
     [,1]
[1,]    7
[2,]   -1
[3,]   -3
[4,]    5
[5,]   17
> x<-solve(A)%*%b
> x
     [,1]
[1,]   -2
[2,]    3
[3,]    5
[4,]    2
[5,]   -4

> mons = c("March","April","January","November","January",
+ "September","October","September","November","August",
+ "January","November","November","February","May","August",
+ "July","December","August","August","September","November",
+ "February","April")
> mons = factor(mons)
> table(mons)
mons
    April    August  December  February   January      July
        2         4         1         2         3         1
    March       May  November   October September
        1         1         5         1         3

ordered=TRUE

> fert = c(10,20,20,50,10,20,10,50,20)
> fert = factor(fert,levels=c(10,20,50),ordered=TRUE)
> fert
[1] 10 20 20 50 10 20 10 50 20
Levels: 10 < 20 < 50