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=Supplementary Explanations of a Basis= | =Supplementary Explanations of a Basis= | ||
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It is important to first check out the [[Basis|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|"span"]], [[Linearly_Independent|"linear independence"]] and [[Subspace|"subspace"]]. | It is important to first check out the [[Basis|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|"span"]], [[Linearly_Independent|"linear independence"]] and [[Subspace|"subspace"]]. | ||
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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? | + | However, what does this mean? Let's say you are given two vectors, <math> |
| + | \begin{pmatrix} | ||
| + | x & y \\ | ||
| + | z & v | ||
| + | \end{pmatrix} | ||
Revision as of 14:22, 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} $
