diff --git a/src/parameters_matrix.jl b/src/parameters_matrix.jl
index d4ced00..55ec0d5 100644
--- a/src/parameters_matrix.jl
+++ b/src/parameters_matrix.jl
@@ -98,7 +98,7 @@ struct PositiveDefinite{TL<:AbstractVector{<:Real},Tε<:Real} <: AbstractParamet
     ε::Tε
 end
 
-Base.:(==)(X::PositiveDefinite, Y::PositiveDefinite) = X.L == Y.L
+Base.:(==)(X::PositiveDefinite, Y::PositiveDefinite) = X.L == Y.L && X.ε == Y.ε
 
 value(X::PositiveDefinite) = A_At(vec_to_tril(X.L)) + X.ε * I
 
diff --git a/test/parameters_matrix.jl b/test/parameters_matrix.jl
index 4f17751..ae86e8c 100644
--- a/test/parameters_matrix.jl
+++ b/test/parameters_matrix.jl
@@ -61,6 +61,8 @@ using ParameterHandling: vec_to_tril, tril_to_vec
         @test isposdef(value(X))
         X.L .= 0 # zero the unconstrained value
         @test isposdef(value(X))
+        @test X != positive_definite(X_mat)
+        @test positive_definite(X_mat, 1e-3) != positive_definite(X_mat, 1e-2)
         @test_throws ArgumentError positive_definite(zeros(3, 3))
         @test_throws ArgumentError positive_definite(X_mat, 0.0)
         test_parameter_interface(X)