# Matrix Multiplication in R

• Last Updated : 17 Jun, 2021

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```

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