diff --git a/src/generics.jl b/src/generics.jl
index 0160558..8613923 100644
--- a/src/generics.jl
+++ b/src/generics.jl
@@ -1,5 +1,9 @@
 # Generic functions (on top of the type-specific implementations)
 
+## constructors
+AbstractPDMat(A::AbstractPDMat) = A
+AbstractPDMat(A::AbstractMatrix) = PDMat(A)
+
 ## arithmetics
 
 pdadd!(r::Matrix, a::Matrix, b::AbstractPDMat{T}) where {T<:Real} = pdadd!(r, a, b, one(T))
diff --git a/src/pdiagmat.jl b/src/pdiagmat.jl
index b9f78fa..9bc0602 100644
--- a/src/pdiagmat.jl
+++ b/src/pdiagmat.jl
@@ -8,6 +8,10 @@ end
 
 PDiagMat(v::AbstractVector{<:Real}) = PDiagMat{eltype(v),typeof(v)}(length(v), v)
 
+AbstractPDMat(A::Diagonal{<:Real}) = PDiagMat(A.diag)
+AbstractPDMat(A::Symmetric{<:Real,<:Diagonal{<:Real}}) = PDiagMat(A.data.diag)
+AbstractPDMat(A::Hermitian{<:Real,<:Diagonal{<:Real}}) = PDiagMat(A.data.diag)
+
 ### Conversion
 Base.convert(::Type{PDiagMat{T}},      a::PDiagMat) where {T<:Real} = PDiagMat(convert(AbstractArray{T}, a.diag))
 Base.convert(::Type{AbstractArray{T}}, a::PDiagMat) where {T<:Real} = convert(PDiagMat{T}, a)
diff --git a/src/pdmat.jl b/src/pdmat.jl
index f4734dc..e543ee9 100644
--- a/src/pdmat.jl
+++ b/src/pdmat.jl
@@ -19,6 +19,8 @@ end
 PDMat(mat::AbstractMatrix) = PDMat(mat, cholesky(mat))
 PDMat(fac::Cholesky) = PDMat(AbstractMatrix(fac), fac)
 
+AbstractPDMat(A::Cholesky) = PDMat(A)
+
 ### Conversion
 Base.convert(::Type{PDMat{T}},         a::PDMat) where {T<:Real} = PDMat(convert(AbstractArray{T}, a.mat))
 Base.convert(::Type{AbstractArray{T}}, a::PDMat) where {T<:Real} = convert(PDMat{T}, a)
diff --git a/src/pdsparsemat.jl b/src/pdsparsemat.jl
index 7c2c433..95ac63a 100644
--- a/src/pdsparsemat.jl
+++ b/src/pdsparsemat.jl
@@ -18,7 +18,10 @@ function PDSparseMat(mat::AbstractSparseMatrix,chol::CholTypeSparse)
 end
 
 PDSparseMat(mat::SparseMatrixCSC) = PDSparseMat(mat, cholesky(mat))
-PDSparseMat(fac::CholTypeSparse) = PDSparseMat(sparse(fac) |> x -> x*x', fac)
+PDSparseMat(fac::CholTypeSparse) = PDSparseMat(sparse(fac), fac)
+
+AbstractPDMat(A::SparseMatrixCSC) = PDSparseMat(A)
+AbstractPDMat(A::CholTypeSparse) = PDSparseMat(A)
 
 ### Conversion
 Base.convert(::Type{PDSparseMat{T}}, a::PDSparseMat) where {T<:Real} = PDSparseMat(convert(SparseMatrixCSC{T}, a.mat))
diff --git a/test/pdmtypes.jl b/test/pdmtypes.jl
index 33ded7e..286288a 100644
--- a/test/pdmtypes.jl
+++ b/test/pdmtypes.jl
@@ -121,4 +121,42 @@ using Test
             @test Matrix(M) ≈ A
         end
     end
+
+    @testset "AbstractPDMat constructors (#136)" begin
+        x = rand(10, 10)
+        A = x' * x + I
+
+        M = @inferred AbstractPDMat(A)
+        @test M isa PDMat
+        @test Matrix(M) ≈ A
+
+        M = @inferred AbstractPDMat(cholesky(A))
+        @test M isa PDMat
+        @test Matrix(M) ≈ A
+
+        M = @inferred AbstractPDMat(Diagonal(A))
+        @test M isa PDiagMat
+        @test Matrix(M) ≈ Diagonal(A)
+
+        M = @inferred AbstractPDMat(Symmetric(Diagonal(A)))
+        @test M isa PDiagMat
+        @test Matrix(M) ≈ Diagonal(A)
+
+        M = @inferred AbstractPDMat(Hermitian(Diagonal(A)))
+        @test M isa PDiagMat
+        @test Matrix(M) ≈ Diagonal(A)
+
+        M = @inferred AbstractPDMat(sparse(A))
+        @test M isa PDSparseMat
+        @test Matrix(M) ≈ A
+
+        if VERSION < v"1.6"
+            # inference fails e.g. on Julia 1.0
+            M = AbstractPDMat(cholesky(sparse(A)))
+        else
+            M = @inferred AbstractPDMat(cholesky(sparse(A)))
+        end
+        @test M isa PDSparseMat
+        @test Matrix(M) ≈ A
+    end
 end
diff --git a/test/testutils.jl b/test/testutils.jl
index 9b194c2..7571583 100644
--- a/test/testutils.jl
+++ b/test/testutils.jl
@@ -91,6 +91,13 @@ function pdtest_basics(C, Cmat::Matrix, d::Int, verbose::Int)
 
     _pdt(verbose, "ishermitian")
     @test ishermitian(C)
+
+    _pdt(verbose, "AbstractPDMat")
+    M = AbstractPDMat(C)
+    @test M isa AbstractPDMat
+    if C isa AbstractPDMat
+        @test M === C
+    end
 end