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| − | In linear algebra, vectors <math>v_1, v_2... v_n</math> form a basis for <math>\ | + | In linear algebra, vectors <math>v_1, v_2... v_n</math> form a basis for <math>\mathbb R^m</math> when |
| − | *The vectors [[span]] <math>\mathbb R^m</math>. (in other words, the span of the vectors is <math>\ | + | *The vectors [[span]] <math>\mathbb R^m</math>. (in other words, the span of the vectors is <math>\mathbb R^m</math>) |
*The vectors are [[Linearly Independent|linearly independent]]. | *The vectors are [[Linearly Independent|linearly independent]]. | ||
Revision as of 16:00, 4 March 2010
In linear algebra, vectors $ v_1, v_2... v_n $ form a basis for $ \mathbb R^m $ when
- The vectors span $ \mathbb R^m $. (in other words, the span of the vectors is $ \mathbb R^m $)
- The vectors are linearly independent.
For a basis, it follows that n must be equal to m.
(Note that there can be more than one set of vectors that form a basis for the same space.)
