1

random_value <- runif(1, min=3, max=10)
n_dims <- as.integer(random_value)
print(n_dims)
## [1] 6
my_vec <- 1:n_dims^2

sample(x=my_vec)
##  [1]  5 26 18 20 24 16 30 36 10 12 33 31 19 28  3 35  1  7 32 34  4 29  9 15 11
## [26] 23  2 21 22 17  8 14  6 27 25 13
m <- matrix(data=my_vec,nrow=n_dims)
print(m)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    7   13   19   25   31
## [2,]    2    8   14   20   26   32
## [3,]    3    9   15   21   27   33
## [4,]    4   10   16   22   28   34
## [5,]    5   11   17   23   29   35
## [6,]    6   12   18   24   30   36
transposed_matrix <- t(m)
print(transposed_matrix)
##      [,1] [,2] [,3] [,4] [,5] [,6]
## [1,]    1    2    3    4    5    6
## [2,]    7    8    9   10   11   12
## [3,]   13   14   15   16   17   18
## [4,]   19   20   21   22   23   24
## [5,]   25   26   27   28   29   30
## [6,]   31   32   33   34   35   36
# switches order of columns and rows

rowSums(m)
## [1]  96 102 108 114 120 126
rowMeans(m)
## [1] 16 17 18 19 20 21
eigen(m)
## eigen() decomposition
## $values
## [1]  1.164118e+02+0.000000e+00i -5.411822e+00+0.000000e+00i
## [3]  4.660296e-15+0.000000e+00i  6.417128e-16+1.832109e-15i
## [5]  6.417128e-16-1.832109e-15i -1.063121e-15+0.000000e+00i
## 
## $vectors
##              [,1]           [,2]          [,3]                    [,4]
## [1,] 0.3542745+0i -0.71909760+0i -0.1342200+0i  0.09720349-0.39400738i
## [2,] 0.3752350+0i -0.50772079+0i  0.4622665+0i -0.05245290+0.05573989i
## [3,] 0.3961956+0i -0.29634399+0i -0.5823752+0i -0.15250865+0.42881785i
## [4,] 0.4171561+0i -0.08496719+0i  0.4864639+0i  0.34950817+0.23031189i
## [5,] 0.4381167+0i  0.12640962+0i -0.4037682+0i -0.51769625+0.00000000i
## [6,] 0.4590772+0i  0.33778642+0i  0.1716330+0i  0.27594614-0.32086225i
##                         [,5]           [,6]
## [1,]  0.09720349+0.39400738i  0.51431380+0i
## [2,] -0.05245290-0.05573989i -0.23908480+0i
## [3,] -0.15250865-0.42881785i -0.76232310+0i
## [4,]  0.34950817-0.23031189i  0.26791247+0i
## [5,] -0.51769625+0.00000000i  0.13591457+0i
## [6,]  0.27594614+0.32086225i  0.08326706+0i
# $values: these numbers are all eigen values of the matrix.

# $vectors: each column of these numbers are eigen vectors, that correspond with the eigen values.

#value
typeof(1.611684e+01)
## [1] "double"
#vector
typeof(-0.4645473)
## [1] "double"

2

my_matrix <- matrix(runif(16), nrow=4, ncol=4)
print(my_matrix)
##           [,1]      [,2]       [,3]       [,4]
## [1,] 0.7160931 0.6868725 0.09250224 0.14478105
## [2,] 0.4509731 0.1023781 0.02280934 0.18741592
## [3,] 0.5435043 0.8476193 0.28703636 0.40819730
## [4,] 0.9927223 0.4026816 0.77642083 0.06197921
my_logical <- runif(100) 
my_logical <- sample(c(TRUE, FALSE), 100, replace = TRUE)
print(my_logical)
##   [1] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE
##  [13]  TRUE  TRUE  TRUE FALSE  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [25] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE
##  [37] FALSE  TRUE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE  TRUE FALSE
##  [49] FALSE  TRUE FALSE  TRUE FALSE FALSE  TRUE  TRUE  TRUE FALSE FALSE  TRUE
##  [61]  TRUE  TRUE FALSE FALSE FALSE  TRUE  TRUE FALSE  TRUE FALSE FALSE  TRUE
##  [73] FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE
##  [85] FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE
##  [97]  TRUE FALSE FALSE FALSE
my_letters <- sample(letters, 26)
print(my_letters)
##  [1] "o" "r" "m" "u" "b" "g" "a" "s" "t" "f" "v" "w" "c" "p" "i" "n" "e" "z" "k"
## [20] "x" "d" "j" "y" "h" "q" "l"
new_list <- c(my_matrix[2,2], my_logical[2], my_letters[1])
print(new_list)
## [1] "0.102378081530333" "FALSE"             "o"
typeof(my_matrix[2,2])
## [1] "double"
typeof(my_logical[2])
## [1] "logical"
typeof(my_logical[2])
## [1] "logical"
typeof(new_list)
## [1] "character"

3

my_unis <- runif(26, min=0, max=10)
print(my_unis)
##  [1] 1.1778697 4.2261954 5.9077959 0.6721664 2.3255471 5.9642698 2.6265242
##  [8] 8.8830906 2.8921987 7.2677753 6.7953497 7.3291572 2.4334676 6.0313015
## [15] 5.1384172 9.7303387 3.3740580 9.9470008 2.6020173 3.1932112 8.1179483
## [22] 5.6048764 8.3914892 4.0927347 4.0058748 3.0068363
my_letters <- sample(LETTERS, 26)
print(my_letters)
##  [1] "F" "W" "U" "Z" "T" "K" "J" "P" "R" "C" "L" "O" "N" "A" "S" "D" "X" "V" "G"
## [20] "Q" "I" "H" "M" "E" "Y" "B"
data_frame <- matrix(c(my_unis, my_letters), nrow=26, ncol=2)
print(data_frame)  
##       [,1]                [,2]
##  [1,] "1.17786972550675"  "F" 
##  [2,] "4.22619544435292"  "W" 
##  [3,] "5.90779592981562"  "U" 
##  [4,] "0.672166370786726" "Z" 
##  [5,] "2.3255470697768"   "T" 
##  [6,] "5.96426978008822"  "K" 
##  [7,] "2.62652424164116"  "J" 
##  [8,] "8.88309059897438"  "P" 
##  [9,] "2.89219874655828"  "R" 
## [10,] "7.26777526549995"  "C" 
## [11,] "6.79534966126084"  "L" 
## [12,] "7.32915719272569"  "O" 
## [13,] "2.43346762377769"  "N" 
## [14,] "6.03130147093907"  "A" 
## [15,] "5.13841721229255"  "S" 
## [16,] "9.730338701047"    "D" 
## [17,] "3.37405803380534"  "X" 
## [18,] "9.94700076524168"  "V" 
## [19,] "2.60201729601249"  "G" 
## [20,] "3.19321115268394"  "Q" 
## [21,] "8.11794827925041"  "I" 
## [22,] "5.60487642418593"  "H" 
## [23,] "8.39148916071281"  "M" 
## [24,] "4.09273470519111"  "E" 
## [25,] "4.00587482377887"  "Y" 
## [26,] "3.00683625042439"  "B"
data_frame[sample(1:nrow(data_frame), 4), 1] <- NA
which(!complete.cases(data_frame))
## [1]  2 10 19 26
str(data_frame)
##  chr [1:26, 1:2] "1.17786972550675" NA "5.90779592981562" ...
my_letters_sorted <- sort(my_letters)
print(my_letters_sorted)
##  [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S"
## [20] "T" "U" "V" "W" "X" "Y" "Z"
data_frame <- matrix(c(my_unis, my_letters_sorted), nrow=26, ncol=2)
print(data_frame)  
##       [,1]                [,2]
##  [1,] "1.17786972550675"  "A" 
##  [2,] "4.22619544435292"  "B" 
##  [3,] "5.90779592981562"  "C" 
##  [4,] "0.672166370786726" "D" 
##  [5,] "2.3255470697768"   "E" 
##  [6,] "5.96426978008822"  "F" 
##  [7,] "2.62652424164116"  "G" 
##  [8,] "8.88309059897438"  "H" 
##  [9,] "2.89219874655828"  "I" 
## [10,] "7.26777526549995"  "J" 
## [11,] "6.79534966126084"  "K" 
## [12,] "7.32915719272569"  "L" 
## [13,] "2.43346762377769"  "M" 
## [14,] "6.03130147093907"  "N" 
## [15,] "5.13841721229255"  "O" 
## [16,] "9.730338701047"    "P" 
## [17,] "3.37405803380534"  "Q" 
## [18,] "9.94700076524168"  "R" 
## [19,] "2.60201729601249"  "S" 
## [20,] "3.19321115268394"  "T" 
## [21,] "8.11794827925041"  "U" 
## [22,] "5.60487642418593"  "V" 
## [23,] "8.39148916071281"  "W" 
## [24,] "4.09273470519111"  "X" 
## [25,] "4.00587482377887"  "Y" 
## [26,] "3.00683625042439"  "Z"