Re: LSI quesitons

[Subbarao Kambhampati <rao@asu.edu>]

At 12:46 AM 2/19/2001 -0700, you wrote:
>         I able to do the singular value decompostion.  Then I chose the
>column of U, V, and S that has the highest number in the S
>diagnol.  But when I try to reconstruct M as M1, my U1,V1, and S1
>vectors aren't compatible for multiplying.  To make it work I have to
>reduce S1 to a scalar, just a number.  Then I get weird answers
>from there on out.  I don't think I am right, is this what you wanted
>for Q4part2, to use k=1?
>



Why wouldn't your U1S1V1' be compatible for multiplying?

Here is how I see it.

U will orginally be a 2x2 matrix (whose columns are the two eigen vectors 
of MM')

S will originally be a 2x2 matrix of signular values

V will originally be a 3x3 matrix of eigen vectors of M'M. Since M'M has 
only two non-zero
eigen vectors, its last column is all zeros and so V will effectely be a 
3x2 matrix.

So  A = U S V' = (2x2) X (2x2) X (2x3) = 2x3

Now after we remove one singular value
U1 is a 2x1 matrix
S1 is a 1x1 matrix
V1 is a 3x1 matrix (so V1' is a 1x3 matrix)

So A1 = (2x1)X (1x1) X(1x3) = 2x3

Rao