diff --git a/include/albatross/src/models/sparse_gp.hpp b/include/albatross/src/models/sparse_gp.hpp
index c9f4c313..69eae477 100644
--- a/include/albatross/src/models/sparse_gp.hpp
+++ b/include/albatross/src/models/sparse_gp.hpp
@@ -315,6 +315,7 @@ class SparseGaussianProcessRegression
     }
     B.bottomRows(n_new) = A_ldlt.sqrt_solve(K_fu);
     const auto B_qr = B.colPivHouseholderQr();
+    ALBATROSS_ASSERT(B_qr.rank() == B_qr.cols());
 
     // Form:
     //   y_aug = |R_old P_old^T v_old|
@@ -379,8 +380,9 @@ class SparseGaussianProcessRegression
     compute_internal_components(u, features, targets, &A_ldlt, &K_uu_ldlt,
                                 &K_fu, &y);
     const auto B_qr = compute_sigma_qr(K_uu_ldlt, A_ldlt, K_fu);
+    ALBATROSS_ASSERT(B_qr.rank() == B_qr.cols());
 
-    Eigen::VectorXd y_augmented = Eigen::VectorXd::Zero(B_qr.matrixR().rows());
+    Eigen::VectorXd y_augmented = Eigen::VectorXd::Zero(B_qr.rows());
     if (Base::use_async_) {
       y_augmented.topRows(y.size()) = A_ldlt.async_sqrt_solve(y);
     } else {
diff --git a/include/albatross/src/utils/linalg_utils.hpp b/include/albatross/src/utils/linalg_utils.hpp
index 78de0214..be0102f7 100644
--- a/include/albatross/src/utils/linalg_utils.hpp
+++ b/include/albatross/src/utils/linalg_utils.hpp
@@ -20,8 +20,10 @@ get_R(const Eigen::ColPivHouseholderQR<Eigen::MatrixXd> &qr) {
   // Unfortunately the matrixR() method in Eigen's QR decomposition isn't
   // actually the R matrix, it's tall skinny matrix whose lower trapezoid
   // contains internal data, only the upper triangular portion is useful
+  //
+  // https://eigen.tuxfamily.org/dox/classEigen_1_1ColPivHouseholderQR.html#abe18678c6af88786f2902eeaf2483251
   return qr.matrixR()
-      .topRows(qr.matrixR().cols())
+      .topLeftCorner(qr.rank(), qr.rank())
       .template triangularView<Eigen::Upper>();
 }
 
@@ -32,7 +34,9 @@ template <typename MatrixType>
 inline Eigen::MatrixXd sqrt_solve(const Eigen::MatrixXd &R,
                                   const Eigen::VectorXi &permutation_indices,
                                   const MatrixType &rhs) {
-
+  // If `R` is not full-rank, the solve operation below isn't
+  // well-defined.
+  ALBATROSS_ASSERT(R.rows() == rhs.rows());
   Eigen::MatrixXd sqrt(rhs.rows(), rhs.cols());
   for (Eigen::Index i = 0; i < permutation_indices.size(); ++i) {
     sqrt.row(i) = rhs.row(permutation_indices.coeff(i));