diff --git a/test/testhelpers/ImmutableArrays.jl b/test/testhelpers/ImmutableArrays.jl
index 8f2d23be..61c78a6d 100644
--- a/test/testhelpers/ImmutableArrays.jl
+++ b/test/testhelpers/ImmutableArrays.jl
@@ -7,6 +7,8 @@
 
 module ImmutableArrays
 
+using LinearAlgebra
+
 export ImmutableArray
 
 "An immutable wrapper type for arrays."
@@ -28,4 +30,34 @@ AbstractArray{T,N}(A::ImmutableArray{S,N}) where {S,T,N} = ImmutableArray(Abstra
 Base.copy(A::ImmutableArray) = ImmutableArray(copy(A.data))
 Base.zero(A::ImmutableArray) = ImmutableArray(zero(A.data))
 
+Base.:(-)(A::ImmutableArray) = ImmutableArray(-A.data)
+Base.:(+)(A::ImmutableArray, B::ImmutableArray) = ImmutableArray(A.data + B.data)
+Base.:(-)(A::ImmutableArray, B::ImmutableArray) = ImmutableArray(A.data - B.data)
+
+Base.:(*)(A::ImmutableArray, x::Number) = ImmutableArray(A.data * x)
+Base.:(*)(x::Number, A::ImmutableArray) = ImmutableArray(x * A.data)
+
+Base.:(*)(A::ImmutableArray, B::ImmutableArray) = ImmutableArray(A.data * B.data)
+
+function LinearAlgebra.eigen(S::SymTridiagonal{T, <:ImmutableArray{T,1}}) where {T}
+    # Use the underlying data for the eigen computation
+    S2 = SymTridiagonal(diag(S), diag(S,1))
+    eigvals, eigvecs = eigen(S2)
+    return Eigen(ImmutableArray(eigvals), ImmutableArray(eigvecs))
+end
+
+function LinearAlgebra.eigen(S::Symmetric{T, <:ImmutableArray{T,2}}) where {T<:Real}
+    # Use the underlying data for the eigen computation
+    S2 = Symmetric(parent(S).data)
+    eigvals, eigvecs = eigen(S2)
+    return Eigen(ImmutableArray(eigvals), ImmutableArray(eigvecs))
+end
+
+function LinearAlgebra.eigen(S::Hermitian{T, <:ImmutableArray{T,2}}) where {T<:Union{Real,Complex}}
+    # Use the underlying data for the eigen computation
+    S2 = Hermitian(parent(S).data)
+    eigvals, eigvecs = eigen(S2)
+    return Eigen(ImmutableArray(eigvals), ImmutableArray(eigvecs))
+end
+
 end
diff --git a/test/tridiag.jl b/test/tridiag.jl
index 9a90e31b..97777a37 100644
--- a/test/tridiag.jl
+++ b/test/tridiag.jl
@@ -1198,4 +1198,32 @@ end
     @test_throws BoundsError S[LinearAlgebra.BandIndex(0,size(S,1)+1)]
 end
 
+@testset "special functions" begin
+    _dv = Float64[1,-2,3,-4]
+    _ev = Float64[1,2,3]
+    @testset "$(typeof(dv))" for (dv, ev) in ((_dv, _ev), ImmutableArray.((_dv, _ev)))
+        dl = -ev
+        T = Tridiagonal(dl, dv, ev)
+        MT = Matrix(T)
+        S = SymTridiagonal(dv, ev)
+        MS = Matrix(S)
+
+        @testset for f in Any[sin, cos, tan,
+                    asin, acos, atan,
+                    sinh, cosh, tanh,
+                    asinh, acosh, atanh,
+                    exp, log, sqrt, cbrt,
+                    ]
+            @test f(T) ≈ f(MT)
+            @test f(S) ≈ f(MS)
+        end
+        for (ST, MST) in ((S, MS), (T, MT))
+            sT, cT = sincos(ST)
+            sMT, cMT = sincos(MST)
+            @test sT ≈ sMT
+            @test cT ≈ cMT
+        end
+    end
+end
+
 end # module TestTridiagonal