Hello everyone,

I’m currently grappling with a challenging problem involving a linear system that’s consistent but ill-conditioned due to the nature of the matrices involved. I’ve devised a potential solution, but I’m seeking feedback and alternative approaches from the community to ensure robustness and efficiency.

Problem Overview:

I’m dealing with a linear system represented as ( M*A = B ), where matrices ( A ) and ( B ) are both real symmetric positive semi-definite, and the condition number of B guaranteed to be no less than that of A.

(The nullspace of A and B should match **in theory** but not sure if the round-off error will be introduced since the linear system is just a small step within a set of complicate odes.)

Proposed Approach:

To address the ill-conditioning while preserving consistency, I’ve devised the following approach:

```
M = nullspace(B) |> x -> (cholesky(Symmetric(A + x*x'))/B)'
```

Thank you!