section4 - 9/16/11 EE221A Section 4 1 Change of basis...

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EE221A Section 4 9/16/11 1 Change of basis Exercise 1. [LN3, p. 10] Let A : R 3 R 3 be a linear map. Consider B = { b 1 ,b 2 ,b 3 } = 1 0 0 , 0 1 0 , 0 0 1 , C = { c 1 ,c 2 ,c 3 } = 1 1 0 , 0 1 1 , 1 0 1 . Clearly B and C are bases for R 3 . Suppose A maps: A ( b 1 ) = 2 - 1 0 , A ( b 2 ) = 0 0 0 , A ( b 3 ) = 0 4 2 . Write down the matrix representation of A w.r.t. B and then w.r.t. C . Exercise 2. Rank of A T A A R m × n , m n , and rank ( A ) = n . Show that rank ( A T A ) = n. 2 Adjoint Exercise 3. Orthogonal complement. Consider the linear map A : U V . Show that R ( A ) = N ( A * ) . 3 Norms Exercise 4. “Zero norm”. Define the zero norm z ( ·
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This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.

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section4 - 9/16/11 EE221A Section 4 1 Change of basis...

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