Supplementary Explanations of a Basis

It is important to first check out the original basis page for the more rigorous definition of a Basis. If you still don't understand, then come back to this page. This page assumes that one already fully understands the terms "span", "linear independence" and "subspace".

What is a Basis?

From the rigorous definition of a Basis, we know that a group of vectors $ v_1, v_2... v_n $ are defined as a basis of a Subspace V if they fulfill two requirements:

• The vectors span V.
• The vectors are linearly independent.

This previous definition is shamelessly copied from the rigorous definition of a Basis.

However, what does this mean? Let's say you are given two vectors, $ \begin{pmatrix} x & y \\ z & v \end{pmatrix} $