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.
