LinearAlgebra: ignore S.ev[length(S.dv)] in ishermitian(S:SymTridiagonal) (#41089)

Author: Jeffrey Lin

stdlib/LinearAlgebra/src/tridiag.jl

@@ -170,7 +170,7 @@ adjoint(S::SymTridiagonal) = Adjoint(S)
 Base.copy(S::Adjoint{<:Any,<:SymTridiagonal}) = SymTridiagonal(map(x -> copy.(adjoint.(x)), (S.parent.dv, S.parent.ev))...)
 Base.copy(S::Transpose{<:Any,<:SymTridiagonal}) = SymTridiagonal(map(x -> copy.(transpose.(x)), (S.parent.dv, S.parent.ev))...)
 
-ishermitian(S::SymTridiagonal) = isreal(S.dv) && isreal(S.ev)
+ishermitian(S::SymTridiagonal) = isreal(S.dv) && isreal(@view S.ev[begin:length(S.dv) - 1])
 issymmetric(S::SymTridiagonal) = true
 
 function diag(M::SymTridiagonal{<:Number}, n::Integer=0)

stdlib/LinearAlgebra/test/tridiag.jl

@@ -632,6 +632,12 @@ end
     @test !ishermitian(A)
 
     # complex
+    # https://github.com/JuliaLang/julia/pull/41037#discussion_r645524081
+    S = SymTridiagonal(randn(5) .+ 0im, randn(5) .+ 0im)
+    S.ev[end] = im
+    @test issymmetric(S)
+    @test ishermitian(S)
+
     S = SymTridiagonal(randn(5) .+ 1im, randn(4) .+ 1im)
     @test issymmetric(S)
     @test !ishermitian(S)