- #1
daviddoria
- 97
- 0
[tex]
Ax = U \Sigma V^T x
[/tex]
(A is an m by n matrix)
I understand the first two steps,
1) [tex]V^T[/tex] takes x and expresses it in a new basis in R^n (since x is already in R^n, this is simply a rotation)
2) [tex]\Sigma[/tex] takes the result of (1) and stretches it
The third step is where I'm a bit fuzzy...
3) U takes the result of (2) and puts it into R^m. In eigenvalue decomposition, this is just the inverse transformation of V^T, but I always read "this is not the inverse transformation of step 1"
Can someone clarify this last step a bit for me?
Thanks!
Dave
Ax = U \Sigma V^T x
[/tex]
(A is an m by n matrix)
I understand the first two steps,
1) [tex]V^T[/tex] takes x and expresses it in a new basis in R^n (since x is already in R^n, this is simply a rotation)
2) [tex]\Sigma[/tex] takes the result of (1) and stretches it
The third step is where I'm a bit fuzzy...
3) U takes the result of (2) and puts it into R^m. In eigenvalue decomposition, this is just the inverse transformation of V^T, but I always read "this is not the inverse transformation of step 1"
Can someone clarify this last step a bit for me?
Thanks!
Dave