Chapter 10 Matrices in R
10.1 What are Matrices?
Matrices are two-dimensional data structures in R and are arranged in a rectangular layout. Matrices can contain only one data type. We can create matrices of any of the six data types we discussed before. A matrix can also be thought of as a vector in two dimension.
We can usematrix function to create a matrix in R programming. I will suggest using “? matrix” for detailed documentation of matrix function Lets create a matrix with 3 rows and two columns
matrix(1:6,nrow = 3,ncol = 2)## [,1] [,2]
## [1,] 1 4
## [2,] 2 5
## [3,] 3 6What if we don’t specify the number of rows and columns?
matrix(1:6,3,2)## [,1] [,2]
## [1,] 1 4
## [2,] 2 5
## [3,] 3 6As you have guessed from the above output, R will automatically pick the number of rows and columns based on the order of input. Let’s specify one of the dimension (either col or row) and see the output:-
matrix(1:6,ncol=3)## [,1] [,2] [,3]
## [1,] 1 3 5
## [2,] 2 4 6So far we have not assigned any columnname and rowname to matrix. Lets create a matrix M and assign colnames and
M<-matrix(1:20,ncol=4)
colnames(M)<-c("A","B","C","D")
rownames(M)<-c("E","F","G","H","I")Lets check the Matrix “M”
M## A B C D
## E 1 6 11 16
## F 2 7 12 17
## G 3 8 13 18
## H 4 9 14 19
## I 5 10 15 20As you can see from the output, we have successfully assigned names to the colnames we can also call the specific columns now. For example Matrix[rowname,colname] will call the required row and columns by name.
M["F","D"]## [1] 17We can row name field blank in the Matrix[rowname,colname] to call complete column
M[,"D"]## E F G H I
## 16 17 18 19 20As you can see in the above example we have kept the row blank. This will cause the above expression to pick all the values to the corresponding columns We can also access specific elements of vectors by specifying row number and column number Lets say we want to pick specific column and vector from Matrix, say 2nd row and 3rd column
M[2,3]## [1] 1210.2 Extracting Row/Column from Matrices
We can also extract more than one row/column at a time. For example below we extraacted first and third column and second row.
M[2,c(1,3)]## A C
## 2 12So what else can we do with Matrices?
10.3 Operations in Matrices
Let perform some operations in Matrices Let’s create two Matrices M1 and M2 and perform some operations
M1<- matrix(1:15,nrow=5)
M1## [,1] [,2] [,3]
## [1,] 1 6 11
## [2,] 2 7 12
## [3,] 3 8 13
## [4,] 4 9 14
## [5,] 5 10 15M2<- matrix(1:15,nrow=5)
M2## [,1] [,2] [,3]
## [1,] 1 6 11
## [2,] 2 7 12
## [3,] 3 8 13
## [4,] 4 9 14
## [5,] 5 10 1510.3.1 Arithmetic Operation in Matrices
What if we add two matrices? Matrices operations can be performed similar to how arithmetic operations are performed on numbers. However we should be careful with the dimension of the numbers that we are working on:-
Lets create three matrices M1, M2, M3 .
M1<- matrix(1:15,nrow=5)
M1## [,1] [,2] [,3]
## [1,] 1 6 11
## [2,] 2 7 12
## [3,] 3 8 13
## [4,] 4 9 14
## [5,] 5 10 15M2<- matrix(2:16,nrow=5)
M2## [,1] [,2] [,3]
## [1,] 2 7 12
## [2,] 3 8 13
## [3,] 4 9 14
## [4,] 5 10 15
## [5,] 6 11 16M3<-matrix(2:10,nrow=5)## Warning in matrix(2:10, nrow = 5): data length [9] is not a sub-multiple or
## multiple of the number of rows [5]M3## [,1] [,2]
## [1,] 2 7
## [2,] 3 8
## [3,] 4 9
## [4,] 5 10
## [5,] 6 2Arithmetic Operations in Matrices
Additon Operation on Matrices of same dimension
M1+M2## [,1] [,2] [,3]
## [1,] 3 13 23
## [2,] 5 15 25
## [3,] 7 17 27
## [4,] 9 19 29
## [5,] 11 21 31What if want to add Matrices of different dimensions? We can check dimension of Matrices using dim function
dim(M1)## [1] 5 3dim(M3)## [1] 5 2Multiplying Matrices of same dimension The following operation using “*" is element wise:-
M1*M2## [,1] [,2] [,3]
## [1,] 2 42 132
## [2,] 6 56 156
## [3,] 12 72 182
## [4,] 20 90 210
## [5,] 30 110 240What if we want Matrix Multiplication? As an exercise try M1%*%M2 in R console for matrix multiplication and check the result. Once you run the operation you must have got an error message “Error in M1 %*% M2: non-conformable arguments" Why is it so? As a basic rule for matrix multiplication number of rows of Matrix1 should be equal to number of columns in Matrix2 when multiplying Matrix1 with Matrix2. You can check following link mathisfun
M4<- matrix(1:9,nrow=3)
M5<-matrix(10:18,nrow=3)
M4## [,1] [,2] [,3]
## [1,] 1 4 7
## [2,] 2 5 8
## [3,] 3 6 9M5## [,1] [,2] [,3]
## [1,] 10 13 16
## [2,] 11 14 17
## [3,] 12 15 18Lets see result of Matrix Multiplication
M4<- matrix(1:9,nrow=3)
M5<-matrix(10:18,nrow=3)
M4%*%M5## [,1] [,2] [,3]
## [1,] 138 174 210
## [2,] 171 216 261
## [3,] 204 258 312You can see the elementwise operation result in R.
M4*M5## [,1] [,2] [,3]
## [1,] 10 52 112
## [2,] 22 70 136
## [3,] 36 90 162M1/M2## [,1] [,2] [,3]
## [1,] 0.5000000 0.8571429 0.9166667
## [2,] 0.6666667 0.8750000 0.9230769
## [3,] 0.7500000 0.8888889 0.9285714
## [4,] 0.8000000 0.9000000 0.9333333
## [5,] 0.8333333 0.9090909 0.9375000What if one of the matrices’ row or column is shorter than the other? Will recycling occur?
As an exercise create a 3X3 matrices and add it to M1.
10.4 Transposing a Matrix
You may also want to transpose your data in R. This is used to interchange rows and columns i.e rows become columns and columns become rows in new transposed matrix For example: -
M3<-t(M1)
M3## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2 3 4 5
## [2,] 6 7 8 9 10
## [3,] 11 12 13 14 15As you can see from the output, the rows have become columns and the columns have become rows. This can also be used to reshape a DataFrame. We will cover DataFrame in next chapter.
10.5 Common Matrix Operations in R
Sum of rows in Matrix
rowSums(M1)## [1] 18 21 24 27 30Sum of columns in Matrix
colSums(M1)## [1] 15 40 65Mean of rows in Matrix
rowMeans(M1)## [1] 6 7 8 9 1010.6 Naming Matrix row and column
rownames(M4)<-c("A","B","C")
colnames(M4)<-c("D","E","F")
M4## D E F
## A 1 4 7
## B 2 5 8
## C 3 6 9We can also extract specific elements of a Matrix by specifying row and columns
M4[3,] #Extracting third row from Matrix M4## D E F
## 3 6 9M4[,3] #Extracting third column from Matrix M4## A B C
## 7 8 9M4[2,3] #Extracting second row and third column element from Matrix M4## [1] 8For details on Matrix operation you can also install Matrix package from CRAN The Comprehensive R Archive Network