Currently ishermitian(::Diagonal) is defined to be true always, but this is wrong when the entries have nonzero nonreal components.
julia> D=Diagonal([Complex(0.0,1.0)]) 1x1 Base.LinAlg.Diagonal{Complex{Float64}}: 0.0+1.0im julia> ishermitian(D) true julia> D' 1x1 Base.LinAlg.Diagonal{Complex{Float64}}: 0.0-1.0im julia> D'==D false
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