As pointed out on discourse, the eigvals functions and a number of other linalg functions are incorrectly promoting rationals to Float32 rather than Float64.

They are calling promote_type(Float32, typeof(one(T)/norm(one(T)))). The Float32 was added by @andreasnoack in JuliaLang/julia#5526 to ensure that Float16 data was promoted to Float32, and the norm call was added by @andreasnoack in JuliaLang/julia#5652, at which point he changed norm(::Rational) to produce a floating-point result. However, the norm(::Rational) method was subsequently changed back to produce a rational result, at which point this bug was introduced.

A simple fix would be to add a float call here (and in other functions that use this promotion scheme).