What is a free sequence in a Hilbert space?

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Discussion Overview

The discussion revolves around the concept of a "free sequence" in the context of Hilbert spaces, as mentioned in a book on the finite element method. Participants explore the definition and implications of this term, particularly in relation to linear independence and spanning properties.

Discussion Character

  • Conceptual clarification

Main Points Raised

  • One participant inquires about the definition of a free sequence in a Hilbert space, indicating a lack of available resources on the topic.
  • Another participant suggests that "free" might imply something akin to unbounded or independent, prompting further exploration of the term.
  • A later reply clarifies that "free" refers to a sequence of linearly independent vectors that span the entire space, noting that the sequence is not necessarily orthonormal.

Areas of Agreement / Disagreement

Participants appear to reach a consensus on the interpretation of "free" as relating to linear independence, but the initial definition remains somewhat ambiguous, with no formal definition provided in the discussion.

Contextual Notes

The discussion lacks formal definitions and relies on interpretations of the term "free sequence." There is an assumption that the context provided in the book may influence the understanding of the term.

stradlater
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Hi!

I'm reading a book on the finite element method and the author mentions a free and total sequence in a hilbert space. I've been searching the internet, but I just can't find the definition of a free sequence. Does anybody know what it is?

Thanks in advance
 
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Is this book a translation into English from another language?
 
Yes, it's the book Numerical Analysis by Roger Temam. Translated from french.
 
Quote some of the context for these terms and perhaps someone can figure it out. Maybe "free" means something like unbounded or independent.
 
Thanks, linearly independent is exactly what it meant :)
So it's a sequence of linearly independent vectors that span the entire space. It makes sense
because the author states that this sequence is not necessarily orthonormal.
 

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