# Difference between a vector and a scalar in Matlab and Octave

To subtract a vector and a scalar number on Matlab / octave use the subtraction operator (-)

**v+n**

The term v is a vector. The term n is a scalar number.

This operation outputs another vector

$$ \vec{v} - n = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} - n = \begin{pmatrix} a_1 - n \\ a_2 - n \\ a_3 - n \end{pmatrix} $$

The operation subtracts the scalar number n from each element of the vector.

**Note**. The subtraction between a vector and a scalar is called a **scalar subtraction**. This is a different operation than vector subtraction.

## Examples

**Example 1**

Define a vector

>> v=[1;2;3]

v =

1

2

3

Calculate the difference between the vector and the scalar number 1

>> v-1

ans =

0

1

2

The result is a new vector.

$$ \vec{v} - 1 = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} - 1 = \begin{pmatrix} 1 - 1 \\ 2 - 1 \\ 3 - 1 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix} $$

**Example 2**

Calculate the difference between the scalar number 1 and the vector v

>> 1-v

ans =

0

-1

-2

The result is another vector

$$ 1 - \vec{v} = 1 - \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 1 - 1 \\ 1 - 2 \\ 1 - 3 \end{pmatrix} = \begin{pmatrix} 0 \\ -1 \\ -2 \end{pmatrix} $$

Scalar subtraction is not a commutative operation.

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