R – Matrix Multiplication

R – Matrix Multiplication

To perform matrix multiplication in R, use the multiplication operator %*%. Please note the percentile % symbols surrounding the arithmetic multiplication operator *.

In this tutorial, we will learn how to multiply matrices using Matrix Multiplication operator with the help of examples.

Syntax

The syntax of the expression to multiply matrices A and B is

A %*% B

The expression returns a matrix. The number of columns in matrix A must equal the number of rows in matrix B.

Examples

In the following program, we will create matrices A and B; multiply them using the matrix multiplication operator, and store the result in matrix AB.

example.R

data <- c(1, 2, 3, 0, 1, 2, 0, 0, 1)
A <- matrix(data, nrow = 3, ncol = 3)

data <- c(0, 1, 1, 1, 0, 3, 1, 3, 3)
B <- matrix(data, nrow = 3, ncol = 3)


AB <- A %*% B

print("Matrix A")
print(A)
print("Matrix B")
print(B)
print("Matrix Multiplication Result")
print(AB)

Output

[1] "Matrix A"
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    2    1    0
[3,]    3    2    1
[1] "Matrix B"
     [,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    0    3
[3,]    1    3    3
[1] "Matrix Multiplication Result"
     [,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    2    5
[3,]    3    6   12

Matrix Multiplication operator can be chained. Therefore, we can multiply multiple matrices in a single expression.

Now, let us take three matrices: A, B and C; and find their product ABC.

example.R

data <- c(1, 2, 3, 0, 1, 2, 0, 0, 1)
A <- matrix(data, nrow = 3, ncol = 3)

data <- c(0, 1, 1, 1, 0, 3, 1, 3, 3)
B <- matrix(data, nrow = 3, ncol = 3)

data <- c(1, 1, 0, 1, 0, 0, 1, 0, 1)
C <- matrix(data, nrow = 3, ncol = 3)


AB <- A %*% B %*% C

print("Matrix A")
print(A)
print("Matrix B")
print(B)
print("Matrix C")
print(C)
print("Matrix Multiplication Result")
print(AB)

Output

[1] "Matrix A"
     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    2    1    0
[3,]    3    2    1
[1] "Matrix B"
     [,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    0    3
[3,]    1    3    3
[1] "Matrix C"
     [,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    0    0
[3,]    0    0    1
[1] "Matrix Multiplication Result"
     [,1] [,2] [,3]
[1,]    1    0    1
[2,]    3    1    6
[3,]    9    3   15

Conclusion

In this R Tutorial, we learned how to perform Matrix Multiplication in R, with the help of examples.