supplement_chap_4 - Linear Algebra, Fall 2007...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Extra Materials for Chapter 4 This document is about how to obtain the matrix representation for the same linear transformation under different pairs of bases in the source and target spaces. Definition: Let x = ± x 1 x 2 ! . [ x ] ²± 1 2 ! , ± 3 4 = ± α β ! if and only if x = α ± 1 2 ! + β ± 3 4 ! Thus ± α β ! is called the coordinate of x relative to the basis ²± 1 2 ! , ± 3 4 Similarly, [ x ] ²± 1 0 ! , ± 0 1 = ± x 1 x 2 ! An important identity: ± 1 3 2 4 α β ! = ± x 1 x 2 = α ± 1 2 ! + β ± 3 4 !! That is, ± 1 3 2 4 ! maps [ x ] ²± 1 2 ! , ± 3 4 to [ x ] ²± 1 0 ! , ± 0 1 via multiplication. In other words, ± 1 3 2 4 ! is the transition matrix from [ x ] ²± 1 2 ! , ± 3 4 to [ x ] ²± 1 0 ! , ± 0 1 . This is contrary to your first instinct. Make sure you understand it correctly. Find some examples from the textbook and exercises, or make up some examples and do the actual computation (change from one set of coordinate to another).
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This note was uploaded on 04/18/2010 for the course FINANCE 1231854365 taught by Professor Wuyiling during the Spring '10 term at Nashville State Community College.

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supplement_chap_4 - Linear Algebra, Fall 2007...

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