diff --git a/src/bidiag.jl b/src/bidiag.jl
index 2fb1415..626f04c 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -198,7 +198,13 @@ function Matrix{T}(A::Bidiagonal) where T
     end
     return B
 end
-Matrix(A::Bidiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(A)
+function Matrix(A::Bidiagonal{T}) where {T}
+    if haszero(T)
+        Matrix{promote_type(T, typeof(zero(T)))}(A)
+    else
+        convert(Matrix, [x for x in A])
+    end
+end
 Array(A::Bidiagonal) = Matrix(A)
 promote_rule(::Type{Matrix{T}}, ::Type{<:Bidiagonal{S}}) where {T,S} =
     @isdefined(T) && @isdefined(S) ? Matrix{promote_type(T,S)} : Matrix
diff --git a/src/dense.jl b/src/dense.jl
index e68f7e9..d4186cf 100644
--- a/src/dense.jl
+++ b/src/dense.jl
@@ -114,7 +114,8 @@ norm2(x::Union{Array{T},StridedVector{T}}) where {T<:BlasFloat} =
 Return whether a type `T` has a unique zero element defined using `zero(T)`.
 If a type `M` specializes `zero(M)`, it may also choose to set `haszero(M)` to `true`.
 By default, `haszero` is assumed to be `false`, in which case the zero elements
-are deduced from values rather than the type.
+are deduced from values rather than the type. In general, if a type defines `zero(::Type{MyType})`,
+it should also define `haszero(::Type{MyType}) = true`.
 
 !!! note
     `haszero` is a conservative check that is used to dispatch to
diff --git a/src/diagonal.jl b/src/diagonal.jl
index 280caec..35e4330 100644
--- a/src/diagonal.jl
+++ b/src/diagonal.jl
@@ -113,7 +113,13 @@ Diagonal{T}(D::Diagonal) where {T} = Diagonal{T}(D.diag)
 
 AbstractMatrix{T}(D::Diagonal) where {T} = Diagonal{T}(D)
 AbstractMatrix{T}(D::Diagonal{T}) where {T} = copy(D)
-Matrix(D::Diagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(D)
+function Matrix(D::Diagonal{T}) where {T}
+    if haszero(T)
+        Matrix{promote_type(T, typeof(zero(T)))}(D)
+    else
+        convert(Matrix, [i for i in D])
+    end
+end
 Matrix(D::Diagonal{Any}) = Matrix{Any}(D)
 Array(D::Diagonal{T}) where {T} = Matrix(D)
 function Matrix{T}(D::Diagonal) where {T}
diff --git a/src/tridiag.jl b/src/tridiag.jl
index a24cc50..dd2b95a 100644
--- a/src/tridiag.jl
+++ b/src/tridiag.jl
@@ -148,7 +148,13 @@ function Matrix{T}(M::SymTridiagonal) where T
     end
     return Mf
 end
-Matrix(M::SymTridiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(M)
+function Matrix(M::SymTridiagonal{T}) where {T}
+    if haszero(T)
+        Matrix{promote_type(T, typeof(zero(T)))}(M)
+    else
+        convert(Matrix, [x for x in M])
+    end
+end
 Array(M::SymTridiagonal) = Matrix(M)
 
 size(A::SymTridiagonal) = (n = length(A.dv); (n, n))
@@ -620,7 +626,13 @@ function Matrix{T}(M::Tridiagonal) where {T}
     end
     A
 end
-Matrix(M::Tridiagonal{T}) where {T} = Matrix{promote_type(T, typeof(zero(T)))}(M)
+function Matrix(M::Tridiagonal{T}) where {T}
+    if haszero(T)
+        Matrix{promote_type(T, typeof(zero(T)))}(M)
+    else
+        convert(Matrix, [x for x in M])
+    end
+end
 Array(M::Tridiagonal) = Matrix(M)
 
 similar(M::Tridiagonal, ::Type{T}) where {T} = Tridiagonal(similar(M.dl, T), similar(M.d, T), similar(M.du, T))
diff --git a/test/bidiag.jl b/test/bidiag.jl
index ea4cfcf..ca3a8fb 100644
--- a/test/bidiag.jl
+++ b/test/bidiag.jl
@@ -1164,4 +1164,11 @@ end
     @test opnorm(B, Inf) == opnorm(Matrix(B), Inf)
 end
 
+@testset "Matrix conversion without zero" begin
+    D = Bidiagonal(fill(ones(2,2), 4), fill(ones(2,2), 3), :U)
+    M = Matrix(D)
+    @test M isa Matrix{eltype(D)}
+    @test M == D
+end
+
 end # module TestBidiagonal
diff --git a/test/diagonal.jl b/test/diagonal.jl
index 1cd2e9d..7cc908d 100644
--- a/test/diagonal.jl
+++ b/test/diagonal.jl
@@ -1473,4 +1473,11 @@ end
     @test opnorm(D, Inf) == opnorm(A, Inf)
 end
 
+@testset "Matrix conversion without zero" begin
+    D = Diagonal(fill(ones(2,2), 4))
+    M = Matrix(D)
+    @test M isa Matrix{eltype(D)}
+    @test M == D
+end
+
 end # module TestDiagonal
diff --git a/test/special.jl b/test/special.jl
index 4b91bcf..4202d47 100644
--- a/test/special.jl
+++ b/test/special.jl
@@ -115,6 +115,8 @@ Random.seed!(1)
         struct TypeWithZero end
         Base.promote_rule(::Type{TypeWithoutZero}, ::Type{TypeWithZero}) = TypeWithZero
         Base.convert(::Type{TypeWithZero}, ::TypeWithoutZero) = TypeWithZero()
+        LinearAlgebra.haszero(::Type{TypeWithoutZero}) = true
+        LinearAlgebra.haszero(::Type{TypeWithZero}) = true
         Base.zero(x::Union{TypeWithoutZero, TypeWithZero}) = zero(typeof(x))
         Base.zero(::Type{<:Union{TypeWithoutZero, TypeWithZero}}) = TypeWithZero()
         LinearAlgebra.symmetric(::TypeWithoutZero, ::Symbol) = TypeWithoutZero()
diff --git a/test/tridiag.jl b/test/tridiag.jl
index 4b592a8..78a829a 100644
--- a/test/tridiag.jl
+++ b/test/tridiag.jl
@@ -1099,4 +1099,13 @@ end
     @test opnorm(S, Inf) == opnorm(Matrix(S), Inf)
 end
 
+@testset "Matrix conversion without zero" begin
+    dv, ev = fill(ones(2,2), 2), fill(ones(2,2), 1)
+    for T in (Tridiagonal(ev, dv, ev), SymTridiagonal(dv, ev))
+        M = Matrix(T)
+        @test M isa Matrix
+        @test M == T
+    end
+end
+
 end # module TestTridiagonal