R – Matrices

 

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.

Syntax

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.

Example

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)

# Elements are arranged sequentially by column.
N <- matrix(c(3:14), nrow = 4, byrow = FALSE)
print(N)

# 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)

When we execute the above code, it produces the following result −

    [,1] [,2] [,3]
[1,]    3 4   5
[2,]    6 7   8
[3,]    9 10 11
[4,]   12 13   14
    [,1] [,2] [,3]
[1,]    3 7 11
[2,]    4 8 12
[3,]    5 9 13
[4,]    6 10 14
    col1 col2 col3
row1    3 4   5
row2    6 7   8
row3    9 10 11
row4   12 13   14

Accessing Elements of a Matrix

Elements 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])

# Access the element at 2nd column and 4th row.
print(P[4,2])

# Access only the  2nd row.
print(P[2,])

# Access only the 3rd column.
print(P[,3])

When we execute the above code, it produces the following result −

[1] 5
[1] 13
col1 col2 col3
  6   7 8
row1 row2 row3 row4
  5   8 11   14

Matrix Computations

Various 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.

Matrix Addition & Subtraction

# Create two 2×3 matrices.
matrix1 <- matrix(c(3, 9, 1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Add the matrices.
result <- matrix1 + matrix2
cat(“Result of addition”,“\n”)
print(result)

# Subtract the matrices
result <- matrix1 matrix2
cat(“Result of subtraction”,“\n”)
print(result)

When we execute the above code, it produces the following result −

    [,1] [,2] [,3]
[1,]    3 -1   2
[2,]    9 4   6
    [,1] [,2] [,3]
[1,]    5 0   3
[2,]    2 9   4
Result of addition
    [,1] [,2] [,3]
[1,]    8 -1   5
[2,]   11 13   10
Result of subtraction
    [,1] [,2] [,3]
[1,]   -2 -1   -1
[2,]    7 -5   2

Matrix Multiplication & Division

# Create two 2×3 matrices.
matrix1 <- matrix(c(3, 9, 1, 4, 2, 6), nrow = 2)
print(matrix1)

matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)

# Multiply the matrices.
result <- matrix1 * matrix2
cat(“Result of multiplication”,“\n”)
print(result)

# Divide the matrices
result <- matrix1 / matrix2
cat(“Result of division”,“\n”)
print(result)

When we execute the above code, it produces the following result −

    [,1] [,2] [,3]
[1,]    3 -1   2
[2,]    9 4   6
    [,1] [,2] [,3]
[1,]    5 0   3
[2,]    2 9   4
Result of multiplication
    [,1] [,2] [,3]
[1,]   15 0    6
[2,]   18 36   24
Result of division
    [,1]     [,2] [,3]
[1,]  0.6   -Inf 0.6666667
[2,]  4.5 0.4444444 1.5000000