Unformatted text preview: σ i ˜ u i ˜ v T i , so using the formula for £ E r ¤ we see that £ K g ¤ + £ E r ¤ = n X i =1 ˜ σ i ˜ u i ˜ v T i . Now, since ˜ v n +1 is orthogonal to ˜ v i for k = 1 , . . . , n , it follows that ( £ K g ¤ + £ E r ¤ ) · f − 1 ¸ = − n X i =1 ˜ σ i ˜ u i ˜ v T i 1 ˜ v n +1 ,n +1 ˜ v n +1 = . Note that ± [ E , r ] ± F = ˜ σ n +1 . (b) This can be proven using the fact that ± A ± 2 F = trace( A T A ) where trace( B ) is the trace of the matrix B , equal to the sum of its diagonal elements (or the sum of 83...
View
Full Document
 Fall '11
 Dr.Robin
 Addition, ui vT, newly added term

Click to edit the document details