Linear Algebra ›Vectors ›Zero Vectors

Zero Vectors

There is a special kind of vector which I would like to mention - the so-called zero vector.

The zero vector is a vector whose components all equal 00. It is often denoted as 0⃗\vec{0} (the number zero with the little arrow on top).

A two-dimensional zero vector looks like this:

0⃗=[00].\vec{0} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}.

The zero vector can be obtained by multiplying any vector by 00 (scalar multiplication), or by subtracting a vector from itself:

0v⃗=[0⋅v10⋅v2]=[00]=0⃗,0\vec{v} = \begin{bmatrix} 0 \cdot v_1 \\ 0 \cdot v_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} = \vec{0},

or

v⃗−v⃗=[v1−v1v2−v2]=[00]=0⃗.\vec{v} - \vec{v} = \begin{bmatrix} v_1 - v_1 \\ v_2 - v_2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} = \vec{0}.