What is a free sequence in a Hilbert space?

stradlater · Mar 26, 2011

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

Stephen Tashi · Mar 26, 2011

Is this book a translation into English from another language?

stradlater · Mar 26, 2011

Yes, it's the book Numerical Analysis by Roger Temam. Translated from french.

Stephen Tashi · Mar 26, 2011

Quote some of the context for these terms and perhaps someone can figure it out. Maybe "free" means something like unbounded or independent.

stradlater · Mar 27, 2011

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.

What is a free sequence in a Hilbert space?

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What is a free sequence in a Hilbert space?

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