10 - MATHEMATICS 54 Professor Constantin Teleman 9/29/09...

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MATHEMATICS 54 Professor Constantin Teleman 9/29/09 Lecture 10 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 *Midterm will not cover section 2.5 and 4.7. *Homework for section 4.7 due on Monday. *Eric Wayman’s 2pm section will go to an overflow room. Watch webpage or ask in section tomorrow. *There is a sample exam on the course webpage. Today we will talk about coordinate changes from Chapter 4 around thirty minutes and then we will do a review. LECTURE Coordinate Changes: V is a finite-dimensional vector space. Assume we have chosen a finite basis r b 1 ... r b n 1 n=dim. Recall: this defines a linear isomorphism of V with R n . Aug r v V has a unique expression x 1 b 1 + ... x n b n , x i R Identification with R n + n n n n x x b x b x x x v . . ... . . 1 1 1 1 r r r Given another basis D= r d 1 ... r d n Get new coordinates on V, different identification with R n , want: a formula relating coordinates in B with coordinates in D. 2 1 2 2 1 1 2 1 2 1 1 1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 2 3 1 2 2 3 1 2 2 3 3 2 2 1 3 2 2 1 x x y x x y x x y y D x D y x y D y y y y x x b x b x d y d y = + = = = = = =
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This note was uploaded on 12/01/2009 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.

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10 - MATHEMATICS 54 Professor Constantin Teleman 9/29/09...

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