# Thread: Problems of pseudoinverse and SVD in linear algebra

1. ## Problems of pseudoinverse and SVD in linear algebra

I am trying to find the pseudo inverse and SVD as well as single values for a matrix:

Thus far I have been able to (this is condensed a little) the following:

Matrix A is:
|1 1 -1|
|1 1 -1|

SVD:
Matrix ATA =

| 2 2 -2|
| 2 2 -2|
|-2 -2 2 |

This matrix has rank 2 so it must have a 2-D nullspace and hence 0 is a double eignevalue. That is the eigenvalues I found to be as:
Lamba2,3 =0, Lambda1 =6.

Thus the corresponding orthonormal eigenvectors are:
V1=1/sqrt(3)*(|1|
|1|
|1|)

V2=1/sqrt(2)*(|1 |
|-1|
| 0|)

V3=1/sqrt(6)*(|1|
|1|
|1|)
Now:
Let V=|V1*V2*V3|

The last two found via satisfying x+y-2z=0 and applying Gram Schmidt to get the orthogonal basis.

Sum=(|alpha1 0 0|
| 0 0 0|)*U1=

Av1/sqrt(6)
= 1/sqrt(2)*(|1|
|1|)

Let U2=1/sqrt(2)*(| 1|
|-11|) to be a vector orthogogonal to u1, and set
u1 = to |u1 u2|

I am trying to finish this problem and it asks to find the Single values, SVD, and Pseudo inverse.

2. Hello, Is anybody out there? I have'nt been able to get working on this problem much lately although..."I did" take it through the entire steps "before" I posted the question!

Again,
I seem to have trouble with finding the SVD; Orthogonal vectors made orthonormal but not getting an SVD. Also, my pseudoinverse is not working?

Any suggestions are totally appreciated Thanks!

3. I got this figured out. There was a great link on the UCD site