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