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MATHEMATICS 54
Professor Constantin
Teleman
9/24/09
Lecture 9
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ANNOUNCEMENTS
*There will be a sample midterm online. It might be
posted on line by tomorrow afternoon.
*I know today there is a walkout. But I think it is a
bad time to cancel class before the midterm. So we
will just participate in the walkout mentally.
*Section 4.7 probably will not be on the midterm.
*Section 2.5 will not be on the midterm. But you
should know the content in the “Boot Camp
Handout.”
*Review session from Student Learning Center will
be at 1012pm on Saturday in 101 Morgan.
LECTURE
Last time we introduced notion of the abstract
vector space that claimed “linear algebra works in
abstract vector space just as well as it does in
n
R
”.
*Vocabulary: all known notions (subspace, linear
combination, linear independence, spanning, basis,
linear transformation, kernel=null space, and
range=column space) can be expressed in this
setting.
*Finitedimensionality allows us to identify any
vector space with some
n
R
, after a choice of basis.
Today we will make the finite dimensionality
precise and discuss more about basis, linear
independence, spanning, and linear transformation.
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 Spring '08
 Chorin
 Math

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