Agreed, this would be very helpful as I am currently creating my own solution.

We already have mat.EigenSym, mat.Eigen and mat.SVD for computing these factorizations but I understand the appeal of having optimized versions for 3x3 matrices, so in principle I'm not against this request.

Some random thoughts:

How would the API look like? Would it follow what we have in mat?

In mat, we have some type safety to do symmetric eigendecomposition only for symmetric matrices. Would we need to introduce a SymMat in r3 or would there be a runtime check or something else?

Would the eigendecomposition compute also eigenvectors or only eigenvalues?

mat.SVD gives non-negative singular values while the method from the second reference may return the smallest singular value as negative (to allow U and V be pure rotations). Are we fine with this inconsistency?

How robust are these formulas/algorithms to weird/bad matrices or do they trade it for performance? Good tests would be needed as part of the implementation.