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Unformatted text preview: Extend the given vector to an arbitrary basis of R 3 and perform GramSchmidt, starting with the given vector as the ±rst basis vector. 6.4 Problem 17 Since A is unitary, its columns { v 1 , . . . , v n } form an ONB of C n . Consider the product A ∗ A = I . We can compute the (1 , j ) entry of the product by expressing it as the inner product of v 1 and v j . Using the fact that A is upper triangular, we now deduce that all entries in the ±rst row of A are zero ecept for a 11 . A similar argument using the inner product of v j and v k for k > j is used to prove every entry in the j th row of A are zero except for the entry on the diagonal. (Hint: Use induction on j and k )....
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This note was uploaded on 01/26/2012 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.
 Spring '10
 FUCKHEAD

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