Linear Algebra (confusing sentence in Griffiths)

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SUMMARY

The discussion clarifies the concept of spanning sets and linear independence in the context of Griffiths' "Introduction to Quantum Mechanics" (2nd edition, p. 437). It establishes that a set of vectors spans a space if every vector in that space can be expressed as a linear combination of the set's members. The confusion arises from the misconception that all member vectors must be linearly dependent; however, a set of linearly independent vectors can also span a space, provided they form a basis for that space. The suggested rephrasing emphasizes the correct interpretation of spanning sets.

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mccoy1
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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.
 
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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"
 
sgd37 said:
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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