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Unformatted text preview: Partial Solution Set, Leon 6.4 *************************************************************************** 6.4.1a For z = 4 + 2 i 4 i and w = 2 2 + i , compute k z k , k w k , h z , w i , and h w , z i . Solution : k z k = z H z = 36 = 6, k w k = w H w = 9 = 3, h z , w i = w H z = 4 + 4 i , and h w , z i = z H w = 4 4 i . 6.4.2b Let z 1 = 1 + i 2 1 i 2 , and z 2 = i 2 1 2 . Write the vector z = 2 + 4 i 2 i as a linear combination of z 1 and z 2 . Solution : From part (a) of this exercise, we know that { z 1 , z 2 } is an orthonormal set, so we dont have to work very hard to come up with coefficients c 1 ,c 2 such that z = c 1 z 1 + c 2 z 2 . By Theorem 5.5.2 and the definition of the complex inner product, c 1 = h z , z 1 i = 4, and c 2 = h z , z 2 i = 2 2, thus z = 4 z 1 + 2 2 z 2 . 6.4.3 Let { u 1 , u 2 } be an orthonormal basis for C 2 , and let z = (4 + 2 i ) u 1 + (6 5 i ) u 2 ....
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This note was uploaded on 07/17/2011 for the course MATH 311 taught by Professor Anshelvich during the Spring '08 term at Texas A&M.
 Spring '08
 Anshelvich
 Linear Algebra, Algebra

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