R – Matrices
Matrices are the R objects in which the elements are arranged in a twodimensional 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