# 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 −

``` 5
 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.

```# 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)

result <- matrix1 + matrix2
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
[,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
```