diff --git a/CMakeLists.txt b/CMakeLists.txt
index f4964209..f8ae7644 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -80,11 +80,17 @@ add_subdirectory(src/cpp_bindings)
 
 pybind11_add_module(pyGinkgoBindings ${PYGINKGO_CPP_SOURCES})
 
+pybind11_add_module(pyGinkgoExtensions ${EXTENSIONS_CPP_SOURCES})
+
 target_include_directories(pyGinkgoBindings
                            PRIVATE ${Ginkgo_BINARY_DIR}/include)
+target_include_directories(pyGinkgoExtensions
+                           PRIVATE ${Ginkgo_BINARY_DIR}/include)
 target_link_libraries(pyGinkgoBindings PRIVATE Ginkgo::ginkgo)
+target_link_libraries(pyGinkgoExtensions PRIVATE Ginkgo::ginkgo)
 target_link_libraries(pyGinkgoBindings PUBLIC nlohmann_json::nlohmann_json)
 set_property(TARGET pyGinkgoBindings PROPERTY CXX_STANDARD 14)
+set_property(TARGET pyGinkgoExtensions PROPERTY CXX_STANDARD 14)
 
 # Disable false positive warnings from GCC (>= 12.4 and <
 # 13)(https://gcc.gnu.org/bugzilla/show_bug.cgi?id=115824 and
@@ -94,6 +100,8 @@ if(CMAKE_CXX_COMPILER_ID STREQUAL "GNU"
    AND CMAKE_CXX_COMPILER_VERSION VERSION_LESS 13.0.0)
   target_compile_options(pyGinkgoBindings PRIVATE -Wno-array-bounds
                                                   -Wno-stringop-overread)
+  target_compile_options(pyGinkgoExtensions PRIVATE -Wno-array-bounds
+                                                    -Wno-stringop-overread)
   message(
     WARNING
       "GCC >= 12.4.0 < 13 gives false positive warning, so we need to add \
diff --git a/src/cpp_bindings/CMakeLists.txt b/src/cpp_bindings/CMakeLists.txt
index b506ac87..3194189b 100644
--- a/src/cpp_bindings/CMakeLists.txt
+++ b/src/cpp_bindings/CMakeLists.txt
@@ -19,3 +19,7 @@ set(PYGINKGO_CPP_SOURCES
     ${PROJECT_SOURCE_DIR}/src/cpp_bindings/solver/triangular.cpp
     ${PROJECT_SOURCE_DIR}/src/cpp_bindings/factorization/factorization.cpp
     PARENT_SCOPE)
+
+set(EXTENSIONS_CPP_SOURCES
+    ${PROJECT_SOURCE_DIR}/src/cpp_bindings/pylinop.cpp
+    PARENT_SCOPE)
diff --git a/src/cpp_bindings/pylinop.cpp b/src/cpp_bindings/pylinop.cpp
new file mode 100644
index 00000000..cca64ec6
--- /dev/null
+++ b/src/cpp_bindings/pylinop.cpp
@@ -0,0 +1,94 @@
+// SPDX-FileCopyrightText: 2026 pyGinkgo authors
+//
+// SPDX-License-Identifier: MIT
+
+#include <iostream>
+
+#include <ginkgo/ginkgo.hpp>
+
+#include <pybind11/pybind11.h>
+
+
+namespace py = pybind11;
+
+
+namespace gko {
+
+
+class PyLinOp : public EnableLinOp<PyLinOp> {
+public:
+    friend class EnableLinOp<PyLinOp>;
+    friend class EnablePolymorphicObject<PyLinOp, LinOp>;
+
+public:
+    void apply_impl(const gko::LinOp *b, gko::LinOp *x) const override
+    {
+        GKO_NOT_IMPLEMENTED;
+    }
+
+    void apply_impl(const gko::LinOp *alpha, const gko::LinOp *b,
+                    const gko::LinOp *beta, gko::LinOp *x) const override
+    {
+        GKO_NOT_IMPLEMENTED;
+    }
+
+    explicit PyLinOp(std::shared_ptr<const gko::Executor> exec,
+                     gko::dim<2> dim = gko::dim<2>{})
+        : gko::EnableLinOp<PyLinOp>(std::move(exec), dim)
+    {}
+};
+
+
+class PyLinOpTrampoline : public PyLinOp {
+    using PyLinOp::PyLinOp;
+
+public:
+    void apply_impl(const gko::LinOp *b, gko::LinOp *x) const override
+    {
+        PYBIND11_OVERRIDE(void, PyLinOp, apply_impl, b, x);
+    }
+};
+
+
+std::unique_ptr<PyLinOp> create(std::shared_ptr<const gko::Executor> exec)
+{
+    return std::unique_ptr<PyLinOp>{new PyLinOpTrampoline{exec}};
+}
+
+std::unique_ptr<PyLinOp> create(std::shared_ptr<const gko::Executor> exec,
+                                gko::dim<2> dim)
+{
+    return std::unique_ptr<PyLinOp>{new PyLinOpTrampoline{exec, dim}};
+}
+
+
+}  // namespace gko
+
+
+class Publicist
+    : public gko::LinOp {  // helper type for exposing protected functions
+public:
+    using gko::LinOp::apply_impl;  // inherited with different access modifier
+};
+
+PYBIND11_MODULE(pyGinkgoExtensions, m, py::mod_gil_not_used())
+{
+    py::class_<gko::PyLinOp, gko::LinOp, gko::PyLinOpTrampoline,
+               std::shared_ptr<gko::PyLinOp>>(m, "PyLinOp")
+        .def(py::init([](std::shared_ptr<const gko::Executor> exec) {
+            auto A = std::shared_ptr(create(exec));
+            return A;
+        }))
+        .def(py::init(
+            [](std::shared_ptr<const gko::Executor> exec, py::tuple dim) {
+                auto A = std::shared_ptr(create(
+                    exec,
+                    gko::dim<2>{dim[0].cast<size_t>(), dim[1].cast<size_t>()}));
+                return A;
+            }))
+        .def("apply_impl", py::overload_cast<const gko::LinOp *, gko::LinOp *>(
+                               &Publicist::apply_impl, py::const_));
+
+    m.def("call_apply", [](const gko::LinOp *linop, const gko::LinOp *b,
+                           gko::LinOp *x) { linop->apply(b, x); });
+}
diff --git a/tests/cpp_bindings/CMakeLists.txt b/tests/cpp_bindings/CMakeLists.txt
index 61dbf654..3beb8bd9 100644
--- a/tests/cpp_bindings/CMakeLists.txt
+++ b/tests/cpp_bindings/CMakeLists.txt
@@ -25,6 +25,7 @@ pyginkgo_bindings_test(iterative_solver)
 pyginkgo_bindings_test(direct_solver)
 pyginkgo_bindings_test(torch)
 pyginkgo_bindings_test(factorization)
+pyginkgo_bindings_test(pylinop)
 
 # add CUDA specific tests, if building with CUDA enabled
 if(GINKGO_BUILD_CUDA)