9 - MATHEMATICS 54 Professor Constantin Teleman 9/24/09...

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MATHEMATICS 54 Professor Constantin Teleman 9/24/09 Lecture 9 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. 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 10-12pm 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. *Finite-dimensionality 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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9 - MATHEMATICS 54 Professor Constantin Teleman 9/24/09...

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