diff --git a/lapack/unit_test/Test_Lapack_svd.hpp b/lapack/unit_test/Test_Lapack_svd.hpp
index 9c5c055818..5e8b6377be 100644
--- a/lapack/unit_test/Test_Lapack_svd.hpp
+++ b/lapack/unit_test/Test_Lapack_svd.hpp
@@ -17,15 +17,81 @@
 #include <gtest/gtest.h>
 #include <Kokkos_Core.hpp>
 #include <KokkosKernels_TestUtils.hpp>
+#include <KokkosBlas3_gemm.hpp>
 
 #include <KokkosLapack_svd.hpp>
 
-#if defined(KOKKOSKERNELS_ENABLE_TPL_CUSOLVER)
-#include "KokkosLapack_cusolver.hpp"
-#endif
-
 namespace Test {
 
+template <class AMatrix, class SVector, class UMatrix, class VMatrix>
+void check_triple_product(const AMatrix& A, const SVector& S, const UMatrix& U, const VMatrix& Vt) {
+  // After a successful SVD decomposition we have A=U*S*V
+  // So using gemm we should be able to compare the above
+  // triple product to the original matrix A.
+
+  using scalar_type = typename AMatrix::non_const_value_type;
+  using mag_type    = typename Kokkos::ArithTraits<scalar_type>::mag_type;
+
+  AMatrix temp("intermediate U*S product", A.extent(0), A.extent(1));
+  AMatrix M("U*S*V product", A.extent(0), A.extent(1));
+
+  // First compute the left side of the product: temp = U*S
+  KokkosBlas::gemm("N", "N", 1, U, S, 0, temp);
+
+  // Second compute the right side of the product: M = temp*V = U*S*V
+  KokkosBlas::gemm("N", "C", 1, temp, Vt, 0, M);
+
+  typename AMatrix::HostMirror A_h = Kokkos::create_mirror_view(A);
+  typename AMatrix::HostMirror M_h = Kokkos::create_mirror_view(M);
+  Kokkos::deep_copy(A_h, A);
+  Kokkos::deep_copy(M_h, M);
+  constexpr mag_type tol = 100*Kokkos::ArithTraits<scalar_type>::eps();
+  for(int rowIdx = 0; rowIdx < A.extent_int(0); ++rowIdx) {
+    for(int colIdx = 0; colIdx < A.extent_int(1); ++colIdx) {
+      EXPECT_NEAR_KK_REL(A_h(rowIdx, colIdx), M_h(rowIdx, colIdx), tol);
+    }
+  }
+}
+
+template <class Matrix>
+void check_unitary_orthogonal_matrix(const Matrix& M) {
+  // After a successful SVD decomposition the matrices
+  // U and V are unitary matrices. Thus we can check
+  // the property UUt=UtU=I and VVt=VtV=I using gemm.
+
+  using scalar_type = typename Matrix::non_const_value_type;
+  using mag_type    = typename Kokkos::ArithTraits<scalar_type>::mag_type;
+  constexpr mag_type tol = 100*Kokkos::ArithTraits<scalar_type>::eps();
+
+  Matrix I0("M*Mt", M.extent(0), M.extent(0));
+  KokkosBlas::gemm("N", "C", 1, M, M, 0, I0);
+  typename Matrix::HostMirror I0_h = Kokkos::create_mirror_view(I0);
+  Kokkos::deep_copy(I0_h, I0);
+  for(int rowIdx = 0; rowIdx < M.extent_int(0); ++rowIdx) {
+    for(int colIdx = 0; colIdx < M.extent_int(0); ++colIdx) {
+      if(rowIdx == colIdx) {
+	EXPECT_NEAR_KK_REL(I0_h(rowIdx, colIdx), Kokkos::ArithTraits<scalar_type>::one(), tol);
+      } else {
+	EXPECT_NEAR_KK_REL(I0_h(rowIdx, colIdx), Kokkos::ArithTraits<scalar_type>::zero(), tol);
+      }
+    }
+  }
+
+  Matrix I1("Mt*M", M.extent(1), M.extent(1));
+  KokkosBlas::gemm("C", "N", 1, M, M, 0, I1);
+  typename Matrix::HostMirror I1_h = Kokkos::create_mirror_view(I1);
+  Kokkos::deep_copy(I1_h, I1);
+  for(int rowIdx = 0; rowIdx < M.extent_int(1); ++rowIdx) {
+    for(int colIdx = 0; colIdx < M.extent_int(1); ++colIdx) {
+      if(rowIdx == colIdx) {
+	EXPECT_NEAR_KK_REL(I1_h(rowIdx, colIdx), Kokkos::ArithTraits<scalar_type>::one(), tol);
+      } else {
+	EXPECT_NEAR_KK_REL(I1_h(rowIdx, colIdx), Kokkos::ArithTraits<scalar_type>::zero(), tol);
+      }
+    }
+  }
+}
+
 template <class AMatrix, class Device>
 int impl_analytic_svd() {
   using scalar_type = typename AMatrix::value_type;
@@ -34,20 +100,27 @@ int impl_analytic_svd() {
   using KAT_S       = Kokkos::ArithTraits<scalar_type>;
   using KAT_M       = Kokkos::ArithTraits<mag_type>;
 
+  const mag_type mag_zero = KAT_M::zero();
+  const mag_type mag_one  = KAT_M::one();
+  const mag_type eps  = KAT_S::eps();
+
   AMatrix A("A", 2, 2), U("U", 2, 2), Vt("Vt", 2, 2);
   vector_type S("S", 2);
 
   typename AMatrix::HostMirror A_h = Kokkos::create_mirror_view(A);
 
+  // A = [3  0]
+  //     [4  5]
+  // USV = 1/sqrt(10) [1  -3] * sqrt(5) [3  0] *  1/sqrt(2) [ 1  1]
+  //                  [3   1]           [0  1]              [-1  1]
   A_h(0, 0) = 3;
   A_h(1, 0) = 4;
   A_h(1, 1) = 5;
 
   Kokkos::deep_copy(A, A_h);
 
-#if defined(KOKKOSKERNELS_ENABLE_TPL_LAPACK) || defined(KOKKOSKERNELS_ENABLE_TPL_CUSOLVER) || defined(KOKKOSKERNELS_ENABLE_TPL_ROCSOLVER)
-
   KokkosLapack::svd(A, S, U, Vt);
+  // Don't really need to fence here as we deep_copy right after...
 
   typename vector_type::HostMirror S_h = Kokkos::create_mirror_view(S);
   Kokkos::deep_copy(S_h, S);
@@ -58,8 +131,8 @@ int impl_analytic_svd() {
 
   // The singular values for this problem
   // are known: sqrt(45) and sqrt(5)
-  EXPECT_NEAR_KK_REL(S_h(0), static_cast<mag_type>(Kokkos::sqrt(45)), 100*KAT_S::eps());
-  EXPECT_NEAR_KK_REL(S_h(1), static_cast<mag_type>(Kokkos::sqrt( 5)), 100*KAT_S::eps());
+  EXPECT_NEAR_KK_REL(S_h(0), static_cast<mag_type>(Kokkos::sqrt(45)), 100*eps);
+  EXPECT_NEAR_KK_REL(S_h(1), static_cast<mag_type>(Kokkos::sqrt( 5)), 100*eps);
 
   // The singular vectors should be identical
   // or of oposite sign we check the first
@@ -68,20 +141,38 @@ int impl_analytic_svd() {
   std::vector<scalar_type> Uref  = {static_cast<scalar_type>(1 / Kokkos::sqrt(10)), static_cast<scalar_type>(3 / Kokkos::sqrt(10)), static_cast<scalar_type>(-3 / Kokkos::sqrt(10)), static_cast<scalar_type>(1 / Kokkos::sqrt(10))};
   std::vector<scalar_type> Vtref = {static_cast<scalar_type>(1 / Kokkos::sqrt(2)), static_cast<scalar_type>(1 / Kokkos::sqrt(2)), static_cast<scalar_type>(-1 / Kokkos::sqrt(2)), static_cast<scalar_type>(1 / Kokkos::sqrt(2))};
 
-  mag_type sign_vec = (U_h(0, 0) > KAT_S::zero()) ? KAT_M::one() : -KAT_M::one();
-  EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 0), Uref[0], 100*KAT_S::eps());
-  EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 0), Uref[1], 100*KAT_S::eps());
-  sign_vec = (U_h(0, 1) < KAT_S::zero()) ? KAT_M::one() : -KAT_M::one();
-  EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 1), Uref[2], 100*KAT_S::eps());
-  EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 1), Uref[3], 100*KAT_S::eps());
-
-  sign_vec = (Vt_h(0, 0) > KAT_S::zero()) ? KAT_M::one() : -KAT_M::one();
-  EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 0), Vtref[0], 100*KAT_S::eps());
-  EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 0), Vtref[1], 100*KAT_S::eps());
-  sign_vec = (Vt_h(0, 1) < KAT_S::zero()) ? KAT_M::one() : -KAT_M::one();
-  EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 1), Vtref[2], 100*KAT_S::eps());
-  EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 1), Vtref[3], 100*KAT_S::eps());
-#endif
+  // Both rotations and reflections are valid
+  // vector basis so we need to check both signs
+  // to confirm proper SVD was achieved.
+  if constexpr(KAT_S::is_complex) {
+    mag_type sign_vec = (U_h(0, 0).real() > KAT_S::zero().real()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 0), Uref[0], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 0), Uref[1], 100*eps);
+    sign_vec = (U_h(0, 1).real() < KAT_S::zero().real()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 1), Uref[2], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 1), Uref[3], 100*eps);
+
+    sign_vec = (Vt_h(0, 0).real() > KAT_S::zero().real()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 0), Vtref[0], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 0), Vtref[1], 100*eps);
+    sign_vec = (Vt_h(0, 1).real() < KAT_S::zero().real()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 1), Vtref[2], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 1), Vtref[3], 100*eps);
+  } else {
+    mag_type sign_vec = (U_h(0, 0) > KAT_S::zero()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 0), Uref[0], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 0), Uref[1], 100*eps);
+    sign_vec = (U_h(0, 1) < KAT_S::zero()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(0, 1), Uref[2], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*U_h(1, 1), Uref[3], 100*eps);
+
+    sign_vec = (Vt_h(0, 0) > KAT_S::zero()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 0), Vtref[0], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 0), Vtref[1], 100*eps);
+    sign_vec = (Vt_h(0, 1) < KAT_S::zero()) ? mag_one : -mag_one;
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(0, 1), Vtref[2], 100*eps);
+    EXPECT_NEAR_KK_REL(sign_vec*Vt_h(1, 1), Vtref[3], 100*eps);
+  }
 
   return 0;
 }
@@ -144,12 +235,41 @@ int test_svd() {
   return 1;
 }
 
+template <class Scalar, class Device>
+int test_wrapper() {
+
+#if defined(KOKKOSKERNELS_ENABLE_TPL_LAPACK) || defined(KOKKOSKERNELS_ENABLE_TPL_MKL)
+  if constexpr(std::is_same_v<typename Device::memory_space, Kokkos::HostSpace>) {
+    // Using a device side space with LAPACK/MKL
+    return test_svd<Scalar, Device>();
+  }
+#endif
+
+#if defined(KOKKOSKERNELS_ENABLE_TPL_CUSOLVER)
+  if constexpr(std::is_same_v<typename Device::execution_space, Kokkos::Cuda>) {
+    // Using a Cuda device with CUSOLVER
+    return test_svd<Scalar, Device>();
+  }
+#endif
+
+#if defined(KOKKOSKERNELS_ENABLE_TPL_ROCSOLVER)
+  if constexpr(std::is_same_v<typename Device::execution_space, Kokkos::HIP>) {
+    // Using a HIP device with ROCSOLVER
+    return test_svd<Scalar, Device>();
+  }
+#endif
+
+  std::cout << "No TPL support enabled, svd is not tested" << std::endl;
+  return 0;
+
+}
+
 #if defined(KOKKOSKERNELS_INST_FLOAT) || \
     (!defined(KOKKOSKERNELS_ETI_ONLY) && \
      !defined(KOKKOSKERNELS_IMPL_CHECK_ETI_CALLS))
 TEST_F(TestCategory, svd_float) {
   Kokkos::Profiling::pushRegion("KokkosLapack::Test::svd_float");
-  test_svd<float, TestDevice>();
+  test_wrapper<float, TestDevice>();
   Kokkos::Profiling::popRegion();
 }
 #endif
@@ -159,7 +279,7 @@ TEST_F(TestCategory, svd_float) {
      !defined(KOKKOSKERNELS_IMPL_CHECK_ETI_CALLS))
 TEST_F(TestCategory, svd_double) {
   Kokkos::Profiling::pushRegion("KokkosLapack::Test::svd_double");
-  test_svd<double, TestDevice>();
+  test_wrapper<double, TestDevice>();
   Kokkos::Profiling::popRegion();
 }
 #endif
@@ -169,7 +289,7 @@ TEST_F(TestCategory, svd_double) {
      !defined(KOKKOSKERNELS_IMPL_CHECK_ETI_CALLS))
 TEST_F(TestCategory, svd_complex_float) {
   Kokkos::Profiling::pushRegion("KokkosLapack::Test::svd_complex_float");
-  test_svd<Kokkos::complex<float>, TestDevice>();
+  test_wrapper<Kokkos::complex<float>, TestDevice>();
   Kokkos::Profiling::popRegion();
 }
 #endif
@@ -179,7 +299,7 @@ TEST_F(TestCategory, svd_complex_float) {
      !defined(KOKKOSKERNELS_IMPL_CHECK_ETI_CALLS))
 TEST_F(TestCategory, svd_complex_double) {
   Kokkos::Profiling::pushRegion("KokkosLapack::Test::svd_complex_double");
-  test_svd<Kokkos::complex<double>, TestDevice>();
+  test_wrapper<Kokkos::complex<double>, TestDevice>();
   Kokkos::Profiling::popRegion();
 }
 #endif