## requirements for SVD to work

Dear fellows,

during my internship I've stumbled over a problem of analysis. To cut things short some pseudoinverses have to be calculated. For one of them it does not work, s.t. A'*A $\neq$ I.

I just wondered about the requirements to find a pseudoinverse. One of the eigenvalues is zero, but as far as I understand that eigenvalues different than zero are not a requirement.

The matrix under consideration is that one:

A = [1 -1 0; 1 0 -1; 0 -1 1; 0 -1 1];

If anyone could help me that would be really great :).

Cheers and thank you very much in advance,
spookyfw
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 Hey spookyfw and welcome to the forums. I just took a look at the Moore-Penrose pseudo-inverse from a grad linear algebra book and for that pseudo-inverse, the relation ship is that BAB = A and ABA = B. Are you using this one or some other one?
 Hi chiro, thank you very much for your reply. Yes I am using the Moore-Penrose pseudo-inverse. Actually the original problem can be seen in the attached picture. After using the pseudo-inverses it is stated that only the first three systems have a solution, but that there is too little information to solve for A00, B00 and C00. When I am multiplying with the pseudo-inverses I get the unitary matrix on the left hand side, but for the last system. So I wondered how that is related to the last one not having a solution and what the reasoning is. I thought about independence, but there is also row-degeneracy in the matrix of the first system. I hope that this still makes sense. Any idea? spookyfw Attached Thumbnails

## requirements for SVD to work

I'm wondering just as a curiosity, whether you have tried using a least squares approach to get some kind of reference for your solutions?
 hmm..what do you mean by that least square approach? I just wanted to check a solution, I just don't understand the mathematical reason why the last system cannot be solved for A00, B00 and C00. How would you go about the least square approach though?