| Line 13: | Line 13: | ||
This previous definition is shamelessly copied from the rigorous definition of a Basis. | 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, <math> | + | However, what does this mean? Let's say you are given two vectors, |
| − | \begin{pmatrix} | + | <math> \begin{pmatrix} |
x & y \\ | x & y \\ | ||
z & v | z & v | ||
\end{pmatrix} | \end{pmatrix} | ||
| + | </math> | ||
Revision as of 13:22, 11 March 2013
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} $
