# How to calculate element-wise multiplication of vectors in Matlab and Octave

To calculate the element-wise product of two vectors in Matlab / Octave use the operator. *

**v.*w**

The terms v and w are two vectors of the same size.

The result is a vector where each element i is the product of elements i of the original two vectors

$$ \vec{v} \cdot \vec{w} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \\ \vdots \\ v_n \end{pmatrix} \cdot \begin{pmatrix} w_1 \\ w_2 \\ w_3 \\ \vdots \\ w_n \end{pmatrix} = \begin{pmatrix} v_1 \cdot w_1 \\ v_2 \cdot w_2 \\ v_3 \cdot w_3 \\ \vdots \\ v_n \cdot w_n \end{pmatrix} $$

**Note**. This vector multiplication is also known as **Hadamard product**, Schur product or element-wise product.

## Example

Define a vector v

>> v=[1;2;3]

v =

1

2

3

Define another vector w with the same number of elements

>> w=[4;5;6]

w =

4

5

6

Compute the element-wise product of the two vectors

>> v.*w

ans =

4

10

18

Matlab calculates the **component-by-component** product of the elements.

The result is a vector composed of the products of the elements of the two vectors that are in the same position

$$ \vec{v} \cdot \vec{w} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} \cdot \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix} = \begin{pmatrix} 1 \cdot 4 \\ 2 \cdot 5 \\ 3 \cdot 6 \end{pmatrix} = \begin{pmatrix} 4 \\ 10 \\ 18 \end{pmatrix} $$

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