# 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.

Live Demo# 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.

Live Demo# 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

Live Demo# 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

Live Demo# 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