The Matrix in R is the most two-dimensional Data structure. In R Matrix, data is stored in row and columns, and we can access the matrix element using both the row index and column index (like an Excel File).

In this article we will show you, How to Create a Matrix, How to Access and manipulate the Matrix Elements, Performing Arithmetic Operations on Matrices with example

## R Matrix Syntax

The basic syntax of the Matrix in R Programming language is as shown below:

Matrix_Name <- matrix(data, nrow, ncol, byname, dimnames)

If you observe the above syntax, data is a Vector and

**nrow:**Please specify the number of Rows you want to create. For example,will create a Matrix of 3 Rows**nrow = 3****ncol:**Please specify the number of Columns you want to create. For example,will create a Matrix of 2 Columns**ncol = 2****byrow:**It is FALSE by default, but you can as per the requirement. If it is TRUE then Matrix elements will be arranged by Rows**dimnames:**It is used to change the default Row and Column names to more meaningful names.

## R Create Matrix

In this example, we will create a Matrix of 12 element. Following code snippet will show you the most traditional way to create a Matrix.

**R CODE**

# R Create Matrix A <- matrix(c(1:12), nrow = 3, ncol = 4) print(A) # Elements are arranged sequentially by column. B <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = FALSE) print(B) # Elements are arranged sequentially by row. D <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE) print(D)

**OUTPUT**

**ANALYSIS**

Below statement will create a Matrix of 12 elements arranged in three rows and four columns.

A <- matrix(c(1:12), nrow = 3, ncol = 4)

From the above screenshot you can observe that, the elements are arranged in column wise. To show the same, we explicitly specified the * byrow* argument

B <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = FALSE)

Let us change the * byrow* option from FALSE to TRUE to arrange the elements by Row wise

D <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE)

### Simple approach to Create R Matrix

It is not always required to specify **nrow,** and **ncol**

**R CODE**

# Create Matrix in R # It will create a Matrix of 3 Rows and the remaining elements will be arranged Accordingly A <- matrix(c(1:12), nrow = 3) print(A) # It will create a Matrix of 4 Columns and the remaining (row) elements will be arranged Accordingly B <- matrix(c(1:12), ncol = 4) print(B) # It will create a Matrix of 3 rows and 4 Columns D <- matrix(c(1:12), 3, 4) print(D) # It will create a Matrix of 3 rows E <- matrix(c(1:12), 3) print(E) # It will create a Matrix of 4 Rows. To create 4 Columns you have to specifyexplicitly G <- matrix(c(1:12), 4) print(G)ncol = 4

**OUTPUT**

### Create R Matrix using cbind and rbind

In this example, we will show you the another way of creating a Matrix in R programming. * cbind* is used for binding vectors in Columns wise, and the

**r***is used for binding vectors in Row wise*

**bind****R CODE**

# R Create Matrix A <- c(1, 2, 3) B <- c(20, 30, 40) X <- cbind(A, B) print(X) Y <- rbind(A, B) print(Y)

**OUTPUT**

### Defining Row names and Column names for matrix in R

In this example we will show you, How to replace the default names of the Rows and Columns, or define new names to the Rows and Columns in a R matrix. We can achieve the same using *dimnames* as: *x <- matrix(1:12, 4, 3, dimnames = list(rowNames, columnNames) *

**R CODE**

# R Create Matrix A <- matrix(20:31, 3, 4, byrow = TRUE, dimnames = list(c("X", "Y", "Z"), c("A", "B", "C", "D"))) print(A) # Defining Row names and Column names of Matrix in R row.names <- c("Row1", "Row2", "Row3") column.names <-c("Col1", "Col2", "Col3", "Col4") B <- matrix(c(1:12), nrow = 3, dimnames = list(row.names, column.names)) print(B)

**OUTPUT**

### R Vector with Recycling elements

All the above specify examples are working fine because we specify exact elements in Rows and columns such as 12 elements arranged in 3 rows and 4 columns. In this example we will show you, What will happen if we specify less number of element.

**R CODE**

# R Create Matrix A <- matrix(c(44: 46), nrow = 3, ncol = 3) print(A) B <- matrix(c(44: 46), nrow = 3, ncol = 3, byrow = TRUE) print(B)

**OUTPUT**

**ANALYSIS**

Below statement will create a Matrix of 12 elements arranged in three rows and four columns. Here 44, 45, and 46 will be repeated until it finished creating 3*4 matrix

A <- matrix(c(44: 46), nrow = 3, ncol = 3)

From the above screenshot you can observe that, 44, 45, and 46 are arranged column wise. To change the recycling style, we changed the * byrow* option from FALSE to TRUE. This will arrange the elements by Row wise

B <- matrix(c(44: 46), nrow = 3, ncol = 3, byrow = TRUE)

### Important Function for Matrix in R

In R Programming, Class function will define its type and dim function will return the dimensions of the Matrix.

**R CODE**

# Data Type and Dimensions of Matrix in R A <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE) print(A) class(A) dim(A)

**OUTPUT**

## Accessing R Matrix Elements

In R programming, We can use the index position to access the Matrix elements. Using this index value, we can access or alter/change each and every individual element present in the Matrix. Index value starts at 1 and end at n where n is the size of a row or column.

For example, we declare a 6 * 4 matrix, means it will stores 6 row elements and 4 column elements. To access or alter 1^{st} value use Matrix.name[1, 1], to access or alter 2^{nd} row 3^{rd} column value then use Matrix.name[2, 3] and to access the 6^{th} row 4^{th} column then use Matrix.name[6, 4]. Lets see the example for better understanding:

**R CODE**

# Accessing R Matrix Elements A <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE) print(A) # Access the element at 1st row and 2nd column. print(A[1, 2]) # Access the element at 3rd row and 4th column. print(A[3, 4]) # Access only the 2nd row. print(A[2,]) # Access only the 4th column. print(A[, 4]) # Access Complete Matrix. print(A[ , ])

**OUTPUT**

### Accessing Subset of a Matrix in R

In our previous example, we show you, How to access the single element from the Matrix. In this example we will show you, How to access subset of multiple items from the Matrix. To achieve the same we use the R Vector

**TIP:** Negative index position are used to omit those values for Matrix in R programming

**R CODE**

# Accessing R Matrix Elements Subset A <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE) print(A) # Access the elements at 1st, 3rd row and 2nd, 4th column. print(A[c(1, 2), c(3, 4)]) # Access All the element at 2nd and 3rd row. print(A[c(2, 3), ]) # Access All the element at 1st and 4th Column. print(A[ , c(1, 4)]) # Access All the element except 2nd row. print(A[-2, ]) # Access All the element except 2nd row and 3rd Columm. print(A[-2, -3]) # Access All the element except 3rd and 4th Columm. print(A[, c(-3, -4)])

**OUTPUT**

### Accessing R Matrix Elements using Boolean Vector

In this example we declared a Boolean vector and used those Boolean values as the index position to access the Matrix * A* elements. Here, TRUE means access the value, and FALSE means omit.

**R CODE**

# Accessing R Matrix Elements using Boolean Vector A <- matrix(c(1:12), nrow = 3, ncol = 4, byrow = TRUE) print(A) # Access the elements at 1st, 3rd row and 2nd, 4th column. print(A[c(TRUE, FALSE, TRUE), c(FALSE, TRUE, FALSE, TRUE)]) # Access All the element at 1ST AND 2nd row. print(A[c(TRUE, TRUE, FALSE), ]) # Access All the element at 1st and 4th Column. print(A[ , c(FALSE, TRUE)]) # Access the elements at 1st, 2nd row and 2nd, 4th column. print(A[c(1, 2), c(FALSE, TRUE, FALSE, TRUE)])

**OUTPUT**

### Accessing R Matrix Elements using Character Index

In this example we will show you, How to access the Matrix elements using Character Vectors Index values.

From the below code snippet you can observe that, we assigned the Row names and Columns Names. This can help us to extract the Matrix elements using the Row names as the Index values.

# Accessing R Matrix Elements using Char Index # Defining Row names and Column names of Matrix in R row.names <- c("Row1", "Row2", "Row3") column.names <-c("Col1", "Col2", "Col3", "Col4") B <- matrix(c(1:12), nrow = 3, dimnames = list(row.names, column.names)) print(B) # Access the elements at 1st row and 3rd Column. print(B["Row1", "Col3"]) # Access only the 2nd row. print(B["Row2",]) # Access only the 4th column. print(B[, "Col4"]) # Access the elements at 2nd row and 2, 3, 4th Column. print(B["Row2", 2:4]) # Access the elements at 1st, 3rd row and 1, 2, 3rd Column. print(B[c("Row1", "Row2"), 2:4])

**OUTPUT**

## Modify R Matrix Elements

In R programming, We can use the index position to modify the elements in a Matrix. Using this index value, we can access or alter/change each and every individual element present in the vector.

For example, if we declare a 3 * 4 matrix that stores 12 elements (3 rows and 4 column). To access or alter 1^{st} value use Matrix.name[1, 1], to access or alter 2^{nd} row 3^{rd} column value use Matrix.name[2, 3]. Lets see the example for better understanding:

# Modifying Matrix in R Programming A <- matrix(c(1:9), nrow = 3, ncol = 3) print(A) A[2, 2] <- 100 print(A) A[A < 5] <- 222 print(A)

**OUTPUT**

**ANALYSIS**

Below statement will assign 100 to the matrix element at position 2nd row and 2nd column.

A[2, 2] <- 100

Following statement will assign 222 to all the elements whose values are less than 5. Here * A < 5* will check whether the elements in Matrix A is less than 5 or not and if the condition is true then that element will be replaced by 222

A[A < 5] <- 222

## R Matrix Addition and Subtraction

In this example we will show you, How to use R Arithmetic Operators on Matrices to perform arithmetic Operations on Matrix in R programming.

# Addition and Subtraction of Matrix in R Programming # Create 2x3 matrices. a <- matrix( c(15, 34, 38, 44, 75, 93), nrow = 2) b <- matrix( c(10, 20, 30, 40, 50, 60), nrow = 2) print(a) print(b) # Addiing two Matrices print(a + b) # Subtraction One Matrix from another print(a - b)

From the above code snippet * a + b *means (15 + 10, 34 + 20, 38 + 30, 44 + 40, 75 + 50, 93 + 60)

**OUTPUT**

## R Matrix Multiplication and Division

In this example we will show you, How to use R Arithmetic Operators on Matrices to perform R Matrix multiplication and Division.

# R Matrix Multiplication and Division # Create 2x3 matrices. a <- matrix( c(25, 30, 28, 12, 90, 64), nrow = 2) b <- matrix( c(5, 3, 2, 3, 3, 4), nrow = 2) print(a) print(b) # R Matrix Multiplication print(a * b) # Matrix Division print(a / b)

**OUTPUT**

**ANALYSIS**

First we declared two matrices of two rows and three columns

a <- matrix( c(25, 30, 28, 12, 90, 64), nrow = 2) b <- matrix( c(5, 3, 2, 3, 3, 4), nrow = 2)

Next, we performed R matrix multiplication and Division on them. Here * a * b *means (25 * 5, 30 * 3, 28 * 2, 12 * 3, 90 * 3, 64 * 4), and

*means (25 / 5, 30 / 3, 28 / 2, 12 / 3, 90 / 3, 64 / 4)*

**a / b**# Matrix Multiplication print(a * b) # Matrix Division print(a / b)

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