Subtraction of a Vector and a Scalar in MATLAB and Octave

In MATLAB and Octave, to subtract a scalar from a vector, simply use the subtraction operator (-).

v+n

Given:

• v represents a vector.
• n denotes a scalar.

The expression ( v - n) yields:

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

This operation subtracts the scalar "n" from each component of the vector "v".

Note. The subtraction of a scalar from a vector is termed "scalar subtraction." It's crucial to distinguish this from vector subtraction.

Examples

Example 1

Define a vector

>> v=[1;2;3]
v =
1
2
3

Subtract the scalar 1 from vector v

>> v-1
ans =
0
1
2

This results in:

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

Example 2

Subtract vector v from the scalar 1

>> 1-v
ans =
0
-1
-2

This yields:

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

It's important to note that scalar subtraction is not commutative.