laqf07f_sg_Chap_4

# laqf07f_sg_Chap_4 - (b) Instead of given the explicit...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Study Guide for Chapter 4 1. Section 4.1: (a) Understand and and memorize the matrix representations of reﬂections, projec- tions, dilations and rotations. (b) Study examples on linear transformations on function spaces. (c) Study examples on kernels and images of linear transformation. 2. Section 4.2: (a) Given the explicit description of a linear transformation L from V to W (that is, you know what L ( v ) is for any v V ), understand and remember the ‘procedures’ to ﬁnd the matrix representation of L with respect to a given pair of bases on V and W . For this, you need to understand what ’coordinate relative to a basis’ means. Try on a few examples, summarize your conclusion and check if your statement agrees with Theorem 4.2.2.
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Unformatted text preview: (b) Instead of given the explicit description of L , suppose you are only give the matrix representation of L relative to a given pair bases. How do you ﬁnd the matrix representation with respect to another pair of bases? Try to give your answer an interpretation as composition of maps. Verify your answer with 4.2.3, which is a special case. (c) Read carefully on ‘supplement for Chap 4’, where the above is explained through an example. 3. Section 4.3: (a) Identify part (b) of section 4.2 above with Theorem 4.3.1 for the special case V = W . (b) Make an correspondence between Theorem 4.3.1 with ﬁgure 4.3.2 and interpret them as composition of maps (functions). (c) Memorize the deﬁnition of ’similar’ matrices. 1...
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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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