Skip to content
Related Articles

Related Articles

Matrix Multiplication in R

View Discussion
Improve Article
Save Article
  • Last Updated : 17 Jun, 2021
View Discussion
Improve Article
Save Article

Matrix multiplication is the most useful matrix operation. It is widely used in areas such as network theory, transformation of coordinates and many more uses nowadays. A matrix in R can be created using matrix() function and this function takes input vector, nrow, ncol, byrow, dimnames as arguments.
Creating a matrix 
A matrix can be created using matrix() function.
 

Python3




# R program to create a matrix
m <- matrix(1:8, nrow=2)
print(m)

Output: 
 

     [,1] [,2] [,3] [,4]
[1,]    1    3    5    7
[2,]    2    4    6    8

 

Multiplication of Matrices

The multiplication operator * is used for multiplying a matrix by scalar or element-wise multiplication of two matrices.
Multiplication with scalar
If you multiply a matrix with a scalar value, then every element of the matrix will be multiplied with that scalar. 
Example: 
 

Python3




# R program for matrix multiplication
# with a scalar
m <- matrix(1:8, nrow=2)
m <- 2*m  
print(m)

Output: 
 

     [,1] [,2] [,3] [,4]
[1,]    2    6   10   14
[2,]    4    8   12   16

In the above code, the scalar is multiplied with every element of the original matrix. This is how the multiplication process takes place: 
 

2*1=2  2*3=6  2*5=10  2*7=14
2*2=4  2*4=8  2*6=12  2*8=16

Multiplication between Matrices 
When a matrix is multiplied with another matrix, the element-wise multiplication of two matrices take place. All the corresponding elements of both matrices will be multiplied under the condition that both matrices will be of the same dimension. 
Example: 
 

Python3




# R program for matrix multiplication
 
# Creating matrices
m <- matrix(1:8, nrow=2)
n <- matrix(8:15, nrow=2)
 
# Multiplying matrices
print(m*n)

Output: 
 

     [,1] [,2] [,3] [,4]
[1,]    8   30   60   98
[2,]   18   44   78  120

This is how the multiplication process takes place: 
 

1*8=8   3*10=30  5*12=60   7*14=98
2*9=18  4*11=44  6*13=78   8*15=120

Multiplication with Vector
If a matrix is multiplied with a vector then vector will be promoted to either row or column matrix to make two arguments conformable. 
Example: 
 

Python3




# R program for matrix multiplication
 
# Creating matrix
m <- matrix(1:8, nrow=2)  
 
# Creating a vector
vec <- 1:2
 
# Multiplying matrix with vector
print(vec*m)

Output: 
 

     [,1] [,2] [,3] [,4]
[1,]    1    3    5    7
[2,]    4    8   12   16

This is how the multiplication process takes place: 
 

             
1*1=1   1*3=3   1*5=5   1*7=7
2*2=4   2*4=8   2*6=12  2*8=16

Multiplication using %*% operator
The Operator%*% is used for matrix multiplication satisfying the condition that the number of columns in the first matrix is equal to the number of rows in second. If matrix A[M, N] and matrix B[N, Z] are multiplied then the resultant matrix will of dimension M*N. 
Example: 
 

Python3




# R program for matrix multiplication
 
# Creating matrices
m <- matrix(1:8, nrow=2)
n <- matrix(8:15, nrow=4)
 
# Multiplying matrices using operator
print(m %*% n)

Output: 
 

     [,1] [,2]
[1,]  162  226
[2,]  200  280

This is how multiplication takes place: 
 

1*8+3*9+5*10+7*11 = 162      1*12+3*13+5*14+7*15=226
2*8+4*9+6*10+8*11 = 200      2*12+4*13+6*14+8*15=280

 


My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!