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Linear Algebra (confusing sentence in Griffiths)

  • Thread starter mccoy1
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  • #1
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In Griffiths Intro to QM (2nd edn) p437 -on linear independent vectors..
" A collection of vectors is said to span the space if every vector can be written as a linear combination of the members of this set".
Well, does this means all member vectors are linearly dependent because that's what I'm thinking? If so, does this means that all linearly independent vectors don't span the space?
Thanks for the clarification.
 

Answers and Replies

  • #2
213
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that sentence is equivalent to: a set of vectors spans a space if they form a basis for that space. A better phrasing would be " A [set] of vectors is said to span the space if every vector [in the space] can be written as a linear combination of the members of this set"
 
  • #3
117
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that sentence is equivalent to: a set of vectors spans a space if they form a basis for that space. A better phrasing would be " A [set] of vectors is said to span the space if every vector [in the space] can be written as a linear combination of the members of this set"
Yes your explanation makes lot of sense...thank you for your help.
 

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