diff --git a/frontend/eigen_cmath/include/algebra/eigen_cmath.hpp b/frontend/eigen_cmath/include/algebra/eigen_cmath.hpp
index 724ca45e..8cc9bf74 100644
--- a/frontend/eigen_cmath/include/algebra/eigen_cmath.hpp
+++ b/frontend/eigen_cmath/include/algebra/eigen_cmath.hpp
@@ -43,7 +43,8 @@ template <unsigned int SIZE, typename derived_type>
 ALGEBRA_HOST_DEVICE inline auto vector(const Eigen::MatrixBase<derived_type>& m,
                                        std::size_t row, std::size_t col) {
 
-  return m.template block<SIZE, 1>(row, col);
+  return m.template block<SIZE, 1>(static_cast<Eigen::Index>(row),
+                                   static_cast<Eigen::Index>(col));
 }
 
 /// @name Getter functions on @c algebra::eigen::matrix_type
diff --git a/frontend/eigen_eigen/include/algebra/eigen_eigen.hpp b/frontend/eigen_eigen/include/algebra/eigen_eigen.hpp
index 7dbcd183..bcf2e38f 100644
--- a/frontend/eigen_eigen/include/algebra/eigen_eigen.hpp
+++ b/frontend/eigen_eigen/include/algebra/eigen_eigen.hpp
@@ -40,7 +40,8 @@ template <unsigned int SIZE, typename derived_type>
 ALGEBRA_HOST_DEVICE inline auto vector(const Eigen::MatrixBase<derived_type>& m,
                                        std::size_t row, std::size_t col) {
 
-  return m.template block<SIZE, 1>(row, col);
+  return m.template block<SIZE, 1>(static_cast<Eigen::Index>(row),
+                                   static_cast<Eigen::Index>(col));
 }
 
 /// @name Getter functions on @c algebra::eigen::matrix_type
diff --git a/math/cmath/include/algebra/math/algorithms/matrix/determinant/partial_pivot_lud.hpp b/math/cmath/include/algebra/math/algorithms/matrix/determinant/partial_pivot_lud.hpp
index e59d1675..b7b5bd3f 100644
--- a/math/cmath/include/algebra/math/algorithms/matrix/determinant/partial_pivot_lud.hpp
+++ b/math/cmath/include/algebra/math/algorithms/matrix/determinant/partial_pivot_lud.hpp
@@ -41,7 +41,7 @@ struct partial_pivot_lud {
 
     // Get the LU decomposition matrix equal to (L - I) + U
     const auto& lu = decomp_res.lu;
-    const auto& n_pivot = decomp_res.n_pivot;
+    const size_type n_pivot = static_cast<size_type>(decomp_res.n_pivot);
 
     scalar_t det = element_getter_t()(lu, 0, 0);
 
diff --git a/math/cmath/include/algebra/math/algorithms/matrix/inverse/partial_pivot_lud.hpp b/math/cmath/include/algebra/math/algorithms/matrix/inverse/partial_pivot_lud.hpp
index 5ee15fa9..327b69cb 100644
--- a/math/cmath/include/algebra/math/algorithms/matrix/inverse/partial_pivot_lud.hpp
+++ b/math/cmath/include/algebra/math/algorithms/matrix/inverse/partial_pivot_lud.hpp
@@ -1,6 +1,6 @@
 /** Algebra plugins library, part of the ACTS project
  *
- * (c) 2022 CERN for the benefit of the ACTS project
+ * (c) 2022-2023 CERN for the benefit of the ACTS project
  *
  * Mozilla Public License Version 2.0
  */
@@ -50,9 +50,10 @@ struct partial_pivot_lud {
     // Calculate inv(A) = inv(U) * inv(L) * P;
     for (size_type j = 0; j < N; j++) {
       for (size_type i = 0; i < N; i++) {
-        element_getter_t()(inv, i, j) = element_getter_t()(P, 0, i) == j
-                                            ? static_cast<scalar_t>(1.0)
-                                            : static_cast<scalar_t>(0.0);
+        element_getter_t()(inv, i, j) =
+            static_cast<size_type>(element_getter_t()(P, 0, i)) == j
+                ? static_cast<scalar_t>(1.0)
+                : static_cast<scalar_t>(0.0);
 
         for (size_type k = 0; k < i; k++) {
           element_getter_t()(inv, i, j) -=
diff --git a/math/cmath/include/algebra/math/impl/cmath_matrix.hpp b/math/cmath/include/algebra/math/impl/cmath_matrix.hpp
index d76a66c8..eacb5be3 100644
--- a/math/cmath/include/algebra/math/impl/cmath_matrix.hpp
+++ b/math/cmath/include/algebra/math/impl/cmath_matrix.hpp
@@ -1,6 +1,6 @@
 /** Algebra plugins library, part of the ACTS project
  *
- * (c) 2022 CERN for the benefit of the ACTS project
+ * (c) 2022-2023 CERN for the benefit of the ACTS project
  *
  * Mozilla Public License Version 2.0
  */
@@ -67,8 +67,8 @@ struct actor {
   /// Operator setting a block with a vector matrix
   template <size_type ROWS, size_type COLS, class input_matrix_type>
   ALGEBRA_HOST_DEVICE void set_block(input_matrix_type &m,
-                                     const matrix_type<ROWS, COLS> &b, int row,
-                                     int col) {
+                                     const matrix_type<ROWS, COLS> &b,
+                                     size_type row, size_type col) {
     for (size_type i = 0; i < ROWS; ++i) {
       for (size_type j = 0; j < COLS; ++j) {
         element_getter()(m, i + row, j + col) = element_getter()(b, i, j);
@@ -80,8 +80,8 @@ struct actor {
   template <size_type ROWS, template <typename, size_type> class vector_t,
             class input_matrix_type>
   ALGEBRA_HOST_DEVICE void set_block(input_matrix_type &m,
-                                     const vector_t<scalar_t, ROWS> &b, int row,
-                                     int col) {
+                                     const vector_t<scalar_t, ROWS> &b,
+                                     size_type row, size_type col) {
     for (size_type i = 0; i < ROWS; ++i) {
       element_getter()(m, i + row, col) = b[i];
     }
diff --git a/math/cmath/include/algebra/math/impl/cmath_transform3.hpp b/math/cmath/include/algebra/math/impl/cmath_transform3.hpp
index 1e43157f..7e7c9f08 100644
--- a/math/cmath/include/algebra/math/impl/cmath_transform3.hpp
+++ b/math/cmath/include/algebra/math/impl/cmath_transform3.hpp
@@ -191,8 +191,8 @@ struct transform3 {
   ALGEBRA_HOST_DEVICE
   inline bool operator==(const transform3 &rhs) const {
 
-    for (int i = 0; i < 4; i++) {
-      for (int j = 0; j < 4; j++) {
+    for (size_type i = 0; i < 4; i++) {
+      for (size_type j = 0; j < 4; j++) {
         if (matrix_actor().element(_data, i, j) !=
             matrix_actor().element(rhs._data, i, j)) {
           return false;
diff --git a/math/eigen/include/algebra/math/impl/eigen_getter.hpp b/math/eigen/include/algebra/math/impl/eigen_getter.hpp
index c990faf9..73216685 100644
--- a/math/eigen/include/algebra/math/impl/eigen_getter.hpp
+++ b/math/eigen/include/algebra/math/impl/eigen_getter.hpp
@@ -1,6 +1,6 @@
 /** Algebra plugins, part of the ACTS project
  *
- * (c) 2020-2022 CERN for the benefit of the ACTS project
+ * (c) 2020-2023 CERN for the benefit of the ACTS project
  *
  * Mozilla Public License Version 2.0
  */
@@ -108,7 +108,7 @@ struct element_getter {
       Eigen::MatrixBase<derived_type> &m, size_type_1 row,
       size_type_2 col) const {
 
-    return m(row, col);
+    return m(static_cast<Eigen::Index>(row), static_cast<Eigen::Index>(col));
   }
   /// Get const access to a matrix element
   template <typename derived_type, typename size_type_1, typename size_type_2,
@@ -120,12 +120,16 @@ struct element_getter {
       const Eigen::MatrixBase<derived_type> &m, size_type_1 row,
       size_type_2 col) const {
 
-    return m(row, col);
+    return m(static_cast<Eigen::Index>(row), static_cast<Eigen::Index>(col));
   }
 };  // struct element_getter
 
 /// Function extracting an element from a matrix (const)
-template <typename derived_type, typename size_type_1, typename size_type_2>
+template <
+    typename derived_type, typename size_type_1, typename size_type_2,
+    std::enable_if_t<std::is_convertible<size_type_1, Eigen::Index>::value &&
+                         std::is_convertible<size_type_2, Eigen::Index>::value,
+                     bool> = true>
 ALGEBRA_HOST_DEVICE inline auto element(
     const Eigen::MatrixBase<derived_type> &m, size_type_1 row,
     size_type_2 col) {
@@ -134,12 +138,14 @@ ALGEBRA_HOST_DEVICE inline auto element(
 }
 
 /// Function extracting an element from a matrix (non-const)
-template <
-    typename derived_type, typename size_type_1, typename size_type_2,
-    std::enable_if_t<std::is_base_of<Eigen::DenseCoeffsBase<
-                                         derived_type, Eigen::WriteAccessors>,
-                                     Eigen::MatrixBase<derived_type> >::value,
-                     bool> = true>
+template <typename derived_type, typename size_type_1, typename size_type_2,
+          std::enable_if_t<
+              std::is_base_of<
+                  Eigen::DenseCoeffsBase<derived_type, Eigen::WriteAccessors>,
+                  Eigen::MatrixBase<derived_type> >::value &&
+                  std::is_convertible<size_type_1, Eigen::Index>::value &&
+                  std::is_convertible<size_type_2, Eigen::Index>::value,
+              bool> = true>
 ALGEBRA_HOST_DEVICE inline auto &element(Eigen::MatrixBase<derived_type> &m,
                                          size_type_1 row, size_type_2 col) {
 
@@ -161,4 +167,4 @@ struct block_getter {
   }
 };  // struct block_getter
 
-}  // namespace algebra::eigen::math
+}  // namespace algebra::eigen::math
\ No newline at end of file
diff --git a/math/eigen/include/algebra/math/impl/eigen_matrix.hpp b/math/eigen/include/algebra/math/impl/eigen_matrix.hpp
index ec738773..25547151 100644
--- a/math/eigen/include/algebra/math/impl/eigen_matrix.hpp
+++ b/math/eigen/include/algebra/math/impl/eigen_matrix.hpp
@@ -1,6 +1,6 @@
 /** Algebra plugins library, part of the ACTS project
  *
- * (c) 2022 CERN for the benefit of the ACTS project
+ * (c) 2022-2023 CERN for the benefit of the ACTS project
  *
  * Mozilla Public License Version 2.0
  */
@@ -52,7 +52,7 @@ struct actor {
   ALGEBRA_HOST_DEVICE inline scalar_t &element(matrix_type<ROWS, COLS> &m,
                                                size_type_1 row,
                                                size_type_2 col) const {
-    return m(row, col);
+    return m(static_cast<Eigen::Index>(row), static_cast<Eigen::Index>(col));
   }
 
   /// Operator getting one value of a const matrix
@@ -64,7 +64,7 @@ struct actor {
   ALGEBRA_HOST_DEVICE inline scalar_t element(const matrix_type<ROWS, COLS> &m,
                                               size_type_1 row,
                                               size_type_2 col) const {
-    return m(row, col);
+    return m(static_cast<Eigen::Index>(row), static_cast<Eigen::Index>(col));
   }
 
   /// Operator getting a block of a const matrix
@@ -77,7 +77,8 @@ struct actor {
   ALGEBRA_HOST_DEVICE matrix_type<ROWS, COLS> block(const input_matrix_type &m,
                                                     size_type_1 row,
                                                     size_type_2 col) {
-    return m.template block<ROWS, COLS>(row, col);
+    return m.template block<ROWS, COLS>(static_cast<Eigen::Index>(row),
+                                        static_cast<Eigen::Index>(col));
   }
 
   /// Operator setting a block
@@ -90,7 +91,8 @@ struct actor {
   ALGEBRA_HOST_DEVICE void set_block(input_matrix_type &m,
                                      const matrix_type<ROWS, COLS> &b,
                                      size_type_1 row, size_type_2 col) {
-    m.template block<ROWS, COLS>(row, col) = b;
+    m.template block<ROWS, COLS>(static_cast<Eigen::Index>(row),
+                                 static_cast<Eigen::Index>(col)) = b;
   }
 
   // Create zero matrix
@@ -139,4 +141,4 @@ struct actor {
   }
 };
 
-}  // namespace algebra::eigen::matrix
+}  // namespace algebra::eigen::matrix
\ No newline at end of file
diff --git a/math/smatrix/include/algebra/math/impl/smatrix_getter.hpp b/math/smatrix/include/algebra/math/impl/smatrix_getter.hpp
index 37c8054c..f87264a0 100644
--- a/math/smatrix/include/algebra/math/impl/smatrix_getter.hpp
+++ b/math/smatrix/include/algebra/math/impl/smatrix_getter.hpp
@@ -30,7 +30,7 @@ template <typename scalar_t, auto N, std::enable_if_t<N >= 2, bool> = true>
 ALGEBRA_HOST inline scalar_t phi(
     const ROOT::Math::SVector<scalar_t, N> &v) noexcept {
 
-  return TMath::ATan2(v[1], v[0]);
+  return static_cast<scalar_t>(TMath::ATan2(v[1], v[0]));
 }
 
 template <typename scalar_t, class A, auto N,
@@ -38,7 +38,7 @@ template <typename scalar_t, class A, auto N,
 ALGEBRA_HOST inline scalar_t phi(
     const ROOT::Math::VecExpr<A, scalar_t, N> &v) noexcept {
 
-  return TMath::ATan2(v.apply(1), v.apply(0));
+  return static_cast<scalar_t>(TMath::ATan2(v.apply(1), v.apply(0)));
 }
 
 /** This method retrieves theta from a vector, vector base with rows >= 3
@@ -49,7 +49,8 @@ template <typename scalar_t, auto N, std::enable_if_t<N >= 3, bool> = true>
 ALGEBRA_HOST inline scalar_t theta(
     const ROOT::Math::SVector<scalar_t, N> &v) noexcept {
 
-  return TMath::ATan2(TMath::Sqrt(v[0] * v[0] + v[1] * v[1]), v[2]);
+  return static_cast<scalar_t>(
+      TMath::ATan2(TMath::Sqrt(v[0] * v[0] + v[1] * v[1]), v[2]));
 }
 
 template <typename scalar_t, class A, auto N,
@@ -57,9 +58,9 @@ template <typename scalar_t, class A, auto N,
 ALGEBRA_HOST inline scalar_t theta(
     const ROOT::Math::VecExpr<A, scalar_t, N> &v) noexcept {
 
-  return TMath::ATan2(
+  return static_cast<scalar_t>(TMath::ATan2(
       TMath::Sqrt(v.apply(0) * v.apply(0) + v.apply(1) * v.apply(1)),
-      v.apply(2));
+      v.apply(2)));
 }
 
 /** This method retrieves the norm of a vector, no dimension restriction
@@ -69,14 +70,14 @@ ALGEBRA_HOST inline scalar_t theta(
 template <typename scalar_t, auto N>
 ALGEBRA_HOST inline scalar_t norm(const ROOT::Math::SVector<scalar_t, N> &v) {
 
-  return TMath::Sqrt(ROOT::Math::Dot(v, v));
+  return static_cast<scalar_t>(TMath::Sqrt(ROOT::Math::Dot(v, v)));
 }
 
 template <typename scalar_t, class A, auto N>
 ALGEBRA_HOST inline scalar_t norm(
     const ROOT::Math::VecExpr<A, scalar_t, N> &v) {
 
-  return TMath::Sqrt(ROOT::Math::Dot(v, v));
+  return static_cast<scalar_t>(TMath::Sqrt(ROOT::Math::Dot(v, v)));
 }
 
 /** This method retrieves the pseudo-rapidity from a vector or vector base with
@@ -88,7 +89,7 @@ template <typename scalar_t, auto N, std::enable_if_t<N >= 3, bool> = true>
 ALGEBRA_HOST inline scalar_t eta(
     const ROOT::Math::SVector<scalar_t, N> &v) noexcept {
 
-  return TMath::ATanH(v[2] / norm(v));
+  return static_cast<scalar_t>(TMath::ATanH(v[2] / norm(v)));
 }
 
 template <typename scalar_t, class A, auto N,
@@ -96,7 +97,7 @@ template <typename scalar_t, class A, auto N,
 ALGEBRA_HOST inline scalar_t eta(
     const ROOT::Math::VecExpr<A, scalar_t, N> &v) noexcept {
 
-  return TMath::ATanH(v.apply(2) / norm(v));
+  return static_cast<scalar_t>(TMath::ATanH(v.apply(2) / norm(v)));
 }
 
 /** This method retrieves the perpenticular magnitude of a vector with rows >= 2
@@ -107,7 +108,7 @@ template <typename scalar_t, auto N, std::enable_if_t<N >= 2, bool> = true>
 ALGEBRA_HOST inline scalar_t perp(
     const ROOT::Math::SVector<scalar_t, N> &v) noexcept {
 
-  return TMath::Sqrt(v[0] * v[0] + v[1] * v[1]);
+  return static_cast<scalar_t>(TMath::Sqrt(v[0] * v[0] + v[1] * v[1]));
 }
 
 template <typename scalar_t, class A, auto N,
@@ -115,7 +116,8 @@ template <typename scalar_t, class A, auto N,
 ALGEBRA_HOST inline scalar_t perp(
     const ROOT::Math::VecExpr<A, scalar_t, N> &v) noexcept {
 
-  return TMath::Sqrt(v.apply(0) * v.apply(0) + v.apply(1) * v.apply(1));
+  return static_cast<scalar_t>(
+      TMath::Sqrt(v.apply(0) * v.apply(0) + v.apply(1) * v.apply(1)));
 }
 
 /// Functor used to access elements of Vc matrices
diff --git a/tests/common/test_host_basics.hpp b/tests/common/test_host_basics.hpp
index c8fd1c84..b64335b8 100644
--- a/tests/common/test_host_basics.hpp
+++ b/tests/common/test_host_basics.hpp
@@ -151,7 +151,7 @@ TYPED_TEST_P(test_host_basics, matrix64) {
   for (typename TypeParam::size_type i = 0; i < ROWS; ++i) {
     for (typename TypeParam::size_type j = 0; j < COLS; ++j) {
       algebra::getter::element(m, i, j) =
-          static_cast<typename TypeParam::scalar>(0.5 * i + j);
+          0.5f * static_cast<typename TypeParam::scalar>(i + j);
     }
   }
 
@@ -160,7 +160,7 @@ TYPED_TEST_P(test_host_basics, matrix64) {
   for (typename TypeParam::size_type i = 0; i < ROWS; ++i) {
     for (typename TypeParam::size_type j = 0; j < COLS; ++j) {
       const typename TypeParam::scalar ref =
-          static_cast<typename TypeParam::scalar>(0.5 * i + j);
+          0.5f * static_cast<typename TypeParam::scalar>(i + j);
       ASSERT_NEAR(algebra::getter::element(m, i, j), ref, this->m_epsilon);
       ASSERT_NEAR(algebra::getter::element(m_const_ref, i, j), ref,
                   this->m_epsilon);
@@ -564,7 +564,7 @@ TYPED_TEST_P(test_host_basics, transform3) {
   std::array<typename TypeParam::scalar, 16> matray_helper = {
       1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0};
   typename TypeParam::transform3::template array_type<16> matray;
-  for (int i = 0; i < 16; ++i) {
+  for (unsigned int i = 0u; i < 16u; ++i) {
     matray[i] = matray_helper[i];
   }
   typename TypeParam::transform3 trfma(matray);