fix equality of eigen factorizations (JuliaLang#41132)

At least the newly added field `rcondv` may contain `undef` values, so
these can cause the same eigen factorizations not to compare equal. Not
100% sure whether the other fields should be ignored as well, but since
we didn't have them before, it seems at least consistent to ignore them
here.

fixes JuliaDiff/ChainRules.jl#422

stdlib/LinearAlgebra/src/eigen.jl

@@ -685,6 +685,16 @@ function show(io::IO, mime::MIME{Symbol("text/plain")}, F::Union{Eigen,Generaliz
     nothing
 end
 
+function Base.hash(F::Eigen, h::UInt)
+    return hash(F.values, hash(F.vectors, hash(Eigen, h)))
+end
+function Base.:(==)(A::Eigen, B::Eigen)
+    return A.values == B.values && A.vectors == B.vectors
+end
+function Base.isequal(A::Eigen, B::Eigen)
+    return isequal(A.values, B.values) && isequal(A.vectors, B.vectors)
+end
+
 # Conversion methods
 
 ## Can we determine the source/result is Real?  This is not stored in the type Eigen

stdlib/LinearAlgebra/test/eigen.jl

@@ -170,5 +170,11 @@ end
     @test eigmax(A') == eigmax(copy(A'))
 end
 
+@testset "equality of eigen factorizations" begin
+    A = randn(3, 3)
+    @test eigen(A) == eigen(A)
+    @test hash(eigen(A)) == hash(eigen(A))
+    @test isequal(eigen(A), eigen(A))
+end
 
 end # module TestEigen