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Unformatted text preview: 7 M such that b L ( −→ x ) b ≤ M b −→ x b for every n ∈ R . This number can be chosen to satisfy the estimate M ≤ mna max where a max is the maximum absolute value of entries in the matrix representative [ L ] . This is an easy application oF the triangle inequality. Given a vector −→ x = ( v 1 ,... ,v n ), let v max be the maximum absolute value oF the components oF −→ x , and let a ij be the entry in row i , column j oF [ L ], The i th component oF L ( −→ v ) is ( L ( −→ v )) i = a i 1 v 1 + ··· + a in v n so we can write  ( L ( −→ v )) i  ≤  a 1 i  v 1  + ··· +  a in  v n  ≤ na max v max . 7 The least such number is called the operator norm of the mapping, and is denoted b L b...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Approximation, Matrices

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