diff --git a/include/ttl/nn/bits/engines/eigen_impl.hpp b/include/ttl/nn/bits/engines/eigen_impl.hpp
new file mode 100644
index 0000000..44ae472
--- /dev/null
+++ b/include/ttl/nn/bits/engines/eigen_impl.hpp
@@ -0,0 +1,75 @@
+#include <ttl/nn/bits/engines/config.hpp>
+#include <ttl/tensor>
+
+#include <Eigen/Core>
+
+namespace ttl::nn::engines
+{
+template <typename R>
+struct eigen_matrix;
+
+template <>
+struct eigen_matrix<float> {
+    using type = Eigen::MatrixXf;
+};
+
+template <>
+struct eigen_matrix<double> {
+    using type = Eigen::MatrixXd;
+};
+
+template <typename R>
+class eigen_impl
+{
+    using m_ref_t = ttl::matrix_ref<R>;
+    using m_view_t = ttl::matrix_view<R>;
+    using v_ref_t = ttl::vector_ref<R>;
+    using v_view_t = ttl::vector_view<R>;
+
+    using eigen_mat = typename eigen_matrix<R>::type;
+
+    static eigen_mat to(const m_view_t &a)
+    {
+        eigen_mat m(std::get<0>(a.dims()), std::get<1>(a.dims()));
+        return m;
+    }
+
+  public:
+    static void mm(const m_view_t &a, const m_view_t &b, const m_ref_t &c)
+    {
+        // FIXME: copy elison
+        const eigen_mat A = to(a);
+        const eigen_mat B = to(b);
+        eigen_mat C = A * B;
+        std::copy(C.data(), C.data() + c.size(), c.data());
+    }
+
+    static void mmt(const m_view_t &a, const m_view_t &b, const m_ref_t &c)
+    {
+        throw std::runtime_error("TODO");
+    }
+
+    static void mtm(const m_view_t &a, const m_view_t &b, const m_ref_t &c)
+    {
+        throw std::runtime_error("TODO");
+    }
+
+    static void mv(const m_view_t &a, const v_view_t &b, const v_ref_t &c)
+    {
+        throw std::runtime_error("TODO");
+    }
+
+    static void vm(const v_view_t &a, const m_view_t &b, const v_ref_t &c)
+    {
+        throw std::runtime_error("TODO");
+    }
+};
+
+struct eigen;
+
+template <>
+struct backend<eigen> {
+    template <typename R>
+    using type = eigen_impl<R>;
+};
+}  // namespace ttl::nn::engines