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=Supplementary Explanations of a Basis= | =Supplementary Explanations of a Basis= | ||
| − | 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 | + | 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"]]. |
| − | ==What is a Basis== | + | ==What is a Basis?== |
| + | |||
| + | From the rigorous definition of a Basis, we know that a group of vectors <math>v_1, v_2... v_n</math> are defined as a basis of a [[Subspace]] V if they fulfill two requirements: | ||
| + | |||
| + | *The vectors [[span]] V. | ||
| + | *The vectors are [[Linearly Independent|linearly independent]]. | ||
| + | |||
| + | This previous definition is shamelessly copied from the rigorous definition of a Basis. | ||
| + | |||
| + | However, what does this mean? | ||
Revision as of 14:16, 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?
