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 2x3 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 2x3 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

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