dat1 <- c(3,4,5,2,1,3,6,5,4)
matrix1 <- matrix(dat1, nrow = 3, ncol = 3, byrow = TRUE)
matrix1

     [,1] [,2] [,3]
[1,]    3    4    5
[2,]    2    1    3
[3,]    6    5    4


library(MASS)
ginv(matrix1)

           [,1]       [,2]        [,3]
[1,] -0.4074074  0.3333333  0.25925926
[2,]  0.3703704 -0.6666667  0.03703704
[3,] 0.1481481 0.3333333 -0.18518519

eigen(matrix1)

$values

[1] 11.238947 -2.088872 -1.150075

$vectors

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

[1,] -0.6017346 -0.3458537 -0.4307244

[2,] -0.3305706 -0.5288292  0.8445517

[3,] -0.7270754  0.7750644 -0.3181336

> A <- matrix(c(2,3,-2,1,2,2),3,2)
> A

     [,1] [,2]
[1,]    2    1
[2,]    3    2
[3,]   -2    2



> is.matrix(A)

[1] TRUE

> is.vector(A)

[1] FALSE

is.matrix( ) 
is.vector( ) 

> A = matrix( 
+   c(2, 4, 3, 1, 5, 7), # the data elements 
+   nrow=2,              # number of rows 
+   ncol=3,              # number of columns 
+   byrow = TRUE)        # fill matrix by rows 
 
> A                      # print the matrix 
     [,1] [,2] [,3] 
[1,]    2    4    3 
[2,]    1    5    7 
> A[2, 3]      # element at 2nd row, 3rd column 
[1] 7 
> A[2, ]       # the 2nd row 
[1] 1 5 7 
> A[ ,3]       # the 3rd column 
[1] 3 7 
> A[ ,c(1,3)]  # the 1st and 3rd columns 
     [,1] [,2] 
[1,]    2    3 
[2,]    1    7 
> dimnames(A) = list( 
+   c("row1", "row2"),         # row names 
+   c("col1", "col2", "col3")) # column names 
 
> A                 # print A 
     col1 col2 col3 
row1    2    4    3 
row2    1    5    7 
 
> A["row2", "col3"] # element at 2nd row, 3rd column 
[1] 7 

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

> x

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

[1,] "10" "[]" "[[1,2]]"

[2,] "20" "[]" "[[1,3]]"

> 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