Consistency checks missing when constructing linear algebra objects

[bardo84]

see https://discourse.julialang.org/t/consistency-checks-missing-when-constructing-linear-algebra-objects/76419

[stevengj]

In general, this seems reasonable, though we might want to have a flag to turn the checks off, at least for an expensive check like testing whether the Schur vectors are orthonormal.

However, it might be more productive to open an issue for particular constructors, rather than a catch-all for all possible LinearAlgebra constructors (some of which probably already have checks).
Or better yet, open pull requests to add checks to particular constructors.

If we want to have a catch-all issue like this, it really needs to come with a checklist of constructors that need checks, i.e. someone needs to do a survey.

[andreasnoack]

The idea is that users should essentially never construct linear algebra objects by calling the constructors. Instead, you call call schur, eigen, cholesky, etc. If you manually create a Schur then you are in charge of doing it correctly. As @stevengj points out, many checks would be too expensive.