Matrix in R

DATA TYPE:



Graphical Representation of Data Types in R is shown as below:


MATRIX:

Matrix is represented as a two-dimensional structure. It can be created using matrix() function.

CREATING MATRIX:

a<-matrix(data = c(1:16), nrow = 8, ncol = 2, byrow = TRUE,dimnames = NULL)
print(a)

        [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    5    6
[4,]    7    8
[5,]    9   10
[6,]   11   12
[7,]   13   14
[8,]   15   16

nrow-       number of Rows in Matrix
ncol-         number of Column in Matrix
byrow-     Either TRUE or FALSE. If FALSE (the default) the matrix is filled by columns, otherwise                       matrix is filled by rows.
dimnames-Either NULL or List of Length 2. i.e. Rowname and Colum name

#Printing Matrix having byrow=False

a<-matrix(data = c(1:16), nrow = 8, ncol = 2, byrow = FALSE,dimnames =NULL)
print(a)
     [,1] [,2]
[1,]    1    9
[2,]    2   10
[3,]    3   11
[4,]    4   12
[5,]    5   13
[6,]    6   14
[7,]    7   15
[8,]    8   16

#Printing Matrix with Row and Column Names

Row<-c("R1","R2","R3","R4","R5","R6","R7","R8")
Col<-c("C1","C2")
a<-matrix(data = c(1:16), nrow = 8, ncol = 2, byrow = TRUE,dimnames = list(Row,Col))
print(a)

      C1 C2
R1  1  2
R2  3  4
R3  5  6
R4  7  8
R5  9 10
R6 11 12
R7 13 14
R8 15 16

#Creating Matrix with Single Constant Element

Let us create Matrix of 2 rows and 3 columns having constant element 6.
matrix(6,2,3)

     [,1] [,2] [,3]
[1,]    6    6    6
[2,]    6    6    6

#Creating Diagonal Matrix

Diagonal Matrix can be created with Single Constant Element

diag(13,3,3)
     [,1] [,2] [,3]
[1,]   13    0    0
[2,]    0   13    0
[3,]    0    0   13

Also, with different values across the diagonal can be created

diag(c(1,2,3),3,3)
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    2    0
[3,]    0    0    3

#Creating Identity Matrix

Identity matrix is a square matrix having value 1 across the diagonal. 

> diag(1,3,3)
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1

#Creating Student Data Matrix

Let us create Matrix of Student marks in various subject

rwname=c('Anu','Annie','Divya','Radha')
clname=c('Java','C++','Accounts','Stats')
Stud_data<-matrix(data=c(81:96),nrow =4,byrow = TRUE,dimnames =list(rwname,clname))
print(Stud_data)

      Java C++ Accounts Stats
Anu     81  82       83    84
Annie   85  86       87    88
Divya   89  90       91    92
Radha   93  94       95    96

MATRIX MANIPULATION:

1. MATRIX DIMENSION:

The Dimension of the Matrix can be found by dim() function. In the below output 8 indicates the number of Rows and 2 indicates the number of columns in the matrix "a".

dim(a)
[1] 8 2

2.ADDING COLUMN TO THE MATRIX:

Let us add a new column "Data Mining" to the matrix using cbind() function.

Stud_data<-cbind(Stud_data,c(69:72))
colnames(Stud_data)<-c('Java','C++','Accounts','Stats','Data Mining')
print(Stud_data)
      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Divya   89  90       91    92          71
Radha   93  94       95    96          72

A new column "Data Mining" is added.

3.ADDING ROW TO THE MATRIX:

We can add a new row to the matrix using rbind() function.

Stud_data<-rbind(Stud_data,c(89,93,22,55,67))
rownames(Stud_data)<-c('Anu','Annie','Divya','Radha',"Kavi")
print(Stud_data)

      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Divya   89  90       91    92          71
Radha   93  94       95    96          72
Kavi    89  93       22    55          67

A new row "Kavi" is added.

4.ACCESSING ELEMENT OF MATRIX

# Accessing Single Element
print(Stud_data[3,3]) 
[1] 91
print(Stud_data[5,5])
[1] 67

#Print Entire Row
print(Stud_data[2,])
       Java         C++    Accounts       Stats Data Mining 
         85          86          87          88          70 

#Print Entire Column
print(Stud_data[,4])
  Anu Annie Divya Radha  Kavi 
   84    88    92    96    55 

# Print Entire Matrix
print(Stud_data[,])  OR 
Stud_data
      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Divya   89  90       91    92          71
Radha   93  94       95    96          72
Kavi    89  93       22    55          67

5.MATRIX COMPUTATION

We can perform addition, subtraction, multiplication, and division only if the matrix is of the same length.
mt1 <- Stud_data
mt2 <- matrix(c(1:25), nrow = 5)

#Addition

mt3<-mt1+mt2
print(mt3)
      Java C++ Accounts Stats Data Mining
Anu     82  88       94   100          90
Annie   87  93       99   105          92
Divya   92  98      104   110          94
Radha   97 103      109   115          96
Kavi    94 103       37    75          92

#Subtraction

mt4<-mt1-mt2
print(mt4)
      Java C++ Accounts Stats Data Mining
Anu     80  76       72    68          48
Annie   83  79       75    71          48
Divya   86  82       78    74          48
Radha   89  85       81    77          48
Kavi    84  83        7    35          42

#Multiplication

mt5<-mt1*mt2
print(mt5)
      Java C++ Accounts Stats Data Mining
Anu     81 492      913  1344        1449
Annie  170 602     1044  1496        1540
Divya  267 720     1183  1656        1633
Radha  372 846     1330  1824        1728
Kavi   445 930      330  1100        1675

#Division

mt6<-mt1/mt2
print(mt6)
          Java      C++ Accounts    Stats Data Mining
Anu   81.00000 13.66667 7.545455 5.250000    3.285714
Annie 42.50000 12.28571 7.250000 5.176471    3.181818
Divya 29.66667 11.25000 7.000000 5.111111    3.086957
Radha 23.25000 10.44444 6.785714 5.052632    3.000000
Kavi  17.80000  9.30000 1.466667 2.750000    2.680000

6. is.matrix()

is.matrix tests if given input is a matrix.

is.matrix(Stud_data)
[1] TRUE

7. Finding Number of Rows

nrow(Stud_data)
[1] 5

8. Finding Number of Columns

ncol(Stud_data)
[1] 5

9. Finding Number of Element

length(Stud_data)
[1] 25

10. Deleting Row from Matrix

Negative Indexing refers to the deletion in Matrix

print(Stud_data)
      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Divya   89  90       91    92          71
Radha   93  94       95    96          72
Kavi    89  93       22    55          67

Let us delete 3rd row from the Stud_data

Stud_data<-Stud_data[-3,]
print(Stud_data)
      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Radha   93  94       95    96          72
Kavi    89  93       22    55          67

11. Deleting Column from Matrix

Negative Indexing refers to the deletion in Matrix

print(Stud_data)
      Java C++ Accounts Stats Data Mining
Anu     81  82       83    84          69
Annie   85  86       87    88          70
Radha   93  94       95    96          72
Kavi    89  93       22    55          67

Let us delete the first column "Java" from the matrix "Stud_data"

Stud_data<-Stud_data[,-1]
print(Stud_data)
      C++ Accounts Stats Data Mining
Anu    82       83    84          69
Annie  86       87    88          70
Radha  94       95    96          72
Kavi   93       22    55          67

12. Transpose of Matrix

Transposing means changing Rows as Columns and Columns as Rows. Let us transpose the Stud_data matrix

t(Stud_data)
            Anu Annie Radha Kavi
C++          82    86    94   93
Accounts     83    87    95   22
Stats        84    88    96   55
Data Mining  69    70    72   67

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