Matrices are the R objects in which the elements are arranged in a two-dimensional rectangular layout. They contain elements of the same atomic types. Though we can create a matrix containing only characters or only logical values, they are not of much use. We use matrices containing numeric elements to be used in mathematical calculations.
A Matrix is created using the matrix() function.
The basic syntax for creating a matrix in R is −
# matrix(data, nrow, ncol, byrow, dimnames)Following is the description of the parameters used −
data is the input vector which becomes the data elements of the matrix.
nrow is the number of rows to be created.
ncol is the number of columns to be created.
byrow is a logical clue. If TRUE then the input vector elements are arranged by row.
dimname is the names assigned to the rows and columns.
Create a matrix taking a vector of numbers as input.
# Elements are arranged sequentially by row.
M <- matrix(c(3:14), nrow = 4, byrow = TRUE)
print(M)## [,1] [,2] [,3]
## [1,] 3 4 5
## [2,] 6 7 8
## [3,] 9 10 11
## [4,] 12 13 14# Elements are arranged sequentially by column.
N <- matrix(c(3:14), nrow = 4, byrow = FALSE)
print(N)## [,1] [,2] [,3]
## [1,] 3 7 11
## [2,] 4 8 12
## [3,] 5 9 13
## [4,] 6 10 14# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")
P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))
print(P)## col1 col2 col3
## row1 3 4 5
## row2 6 7 8
## row3 9 10 11
## row4 12 13 14Elements of a matrix can be accessed by using the column and row index of the element. We consider the matrix P above to find the specific elements below.
# Define the column and row names.
rownames = c("row1", "row2", "row3", "row4")
colnames = c("col1", "col2", "col3")
# Create the matrix.
P <- matrix(c(3:14), nrow = 4, byrow = TRUE, dimnames = list(rownames, colnames))
# Access the element at 3rd column and 1st row.
print(P[1,3])## [1] 5# Access the element at 2nd column and 4th row.
print(P[4,2])## [1] 13# Access only the 2nd row.
print(P[2,])## col1 col2 col3
## 6 7 8# Access only the 3rd column.
print(P[,3])## row1 row2 row3 row4
## 5 8 11 14Various mathematical operations are performed on the matrices using the R operators. The result of the operation is also a matrix.
The dimensions (number of rows and columns) should be same for the matrices involved in the operation.
# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)## [,1] [,2] [,3]
## [1,] 3 -1 2
## [2,] 9 4 6matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)## [,1] [,2] [,3]
## [1,] 5 0 3
## [2,] 2 9 4# Add the matrices.
result <- matrix1 + matrix2
cat("Result of addition","\n")## Result of additionprint(result)## [,1] [,2] [,3]
## [1,] 8 -1 5
## [2,] 11 13 10# Subtract the matrices
result <- matrix1 - matrix2
cat("Result of subtraction","\n")## Result of subtractionprint(result)## [,1] [,2] [,3]
## [1,] -2 -1 -1
## [2,] 7 -5 2# Create two 2x3 matrices.
matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)## [,1] [,2] [,3]
## [1,] 3 -1 2
## [2,] 9 4 6matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)## [,1] [,2] [,3]
## [1,] 5 0 3
## [2,] 2 9 4# Multiply the matrices.
result <- matrix1 * matrix2
cat("Result of multiplication","\n")## Result of multiplicationprint(result)## [,1] [,2] [,3]
## [1,] 15 0 6
## [2,] 18 36 24# Divide the matrices
result <- matrix1 / matrix2
cat("Result of division","\n")## Result of divisionprint(result)## [,1] [,2] [,3]
## [1,] 0.6 -Inf 0.6666667
## [2,] 4.5 0.4444444 1.5000000