soln05 - Homework 11 September 2006 1 Problem The matrix S...

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Unformatted text preview: Homework 11 September 2006 1 Problem The matrix S given in the file signalsvd.txt is in the form shown below ⎡ ⎤ S ( λ 1 , t 1 ) S ( λ 2 , t 1 ) · · · S ( λ n , t 1 ) ⎢ ⎥ ⎢ S ( λ 1 , t 2 ) S ( λ 2 , t 2 ) · · · S ( λ n , t 2 ) ⎥ ⎢ ⎥ ⎢ ⎥ S = · · · ⎢ ⎥ ⎢ ⎥ ⎣ · · · ⎦ S ( λ 1 , t k ) S ( λ 2 , t k ) · · · S ( λ n , t k ) Signal due to each species can be written as ⎡ ⎤ a i ( λ 1 ) x i ( t 1 ) a i ( λ 2 ) x i ( t 1 ) · · · a i ( λ n ) x i ( t 1 ) ⎢ ⎥ ⎢ a i ( λ 1 ) x i ( t 2 ) a i ( λ 2 ) x i ( t 2 ) · · · a i ( λ n ) x i ( t 2 ) ⎥ ⎢ ⎥ ⎢ ⎥ S i = σ i · · · ⎢ ⎥ ⎢ ⎥ ⎣ · · · ⎦ a i ( λ 1 ) x i ( t n ) a i ( λ 2 ) x i ( t n ) · · · a i ( λ n ) x i ( t k ) where a i and x i are the dimensionless signal strength and concentration of species i respectively. But the above array can be written as a product of two vectors as follows ⎡ ⎤ x i ( t 1 ) ⎢ ⎢ x i ( t 2 ) ⎥ ⎥ ⎢ ⎥ S i = σ i ⎢ ⎢ ⎢ ....
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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soln05 - Homework 11 September 2006 1 Problem The matrix S...

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