How to Define Vectors in Matlab

In this lesson, I will explain how to create a vector in Matlab.

Let's start with a practical example.

Consider a vector on the plane that originates from the point (0;0) and points to the coordinates v(2;4).

An example of a two-dimensional vector (in the plane).

The vector has two components, x=2 and y=4.

To define this vector in Matlab, you need to use a two-dimensional array variable.

In the array, separate the x and y components of the vector using a semicolon.

>> v=[2;4]

This way you define a column vector.

$$ \vec{v} = \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix} $$

You can use the array you just created in any vector computation operation (e.g., vector addition, cross product, dot product, etc.).

To create a vector with three or more components, you can follow the same procedure.

For example, consider a three-dimensional vector (in 3D space) that points to the coordinates v(2;4;3).

An example of a three-dimensional vector (in space).

This vector has three components, x=2, y=4, z=3.

$$ \vec{v} = \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \\ 3 \end{pmatrix} $$

To define this vector in the Matlab environment, create an array with three components.

>> v=[2;4;3]

So far, I have explained how to create a column vector where the elements are arranged vertically.

$$ \vec{v} = \begin{pmatrix} a \\ b \\ c \end{pmatrix} $$

If you need to create a row vector, where the elements are arranged horizontally, you need to use a different syntax.

$$ \vec{v} = \begin{pmatrix} a & b & c \end{pmatrix} $$

To create a row vector in Matlab, create an array and separate the components with a space or a comma.

For example, to define this row vector:

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

Type an array and separate the elements with a comma.

>> v=[1, 2, 3]

The result is a row vector.

Note. Alternatively, you can create a column vector v=[1;2;3] and convert it into a row vector by transposing v