soln05 - Homework 5 11 September 2006 1 Problem 1 The...

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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 . a i ( λ 1 ) a i ( λ 2 ) · · · a i ( λ k ) . .
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