diff --git a/src/eigen/lobpcg_hyper_impl.jl b/src/eigen/lobpcg_hyper_impl.jl
index 44eb12cbc..7f25e9882 100644
--- a/src/eigen/lobpcg_hyper_impl.jl
+++ b/src/eigen/lobpcg_hyper_impl.jl
@@ -298,11 +298,21 @@ end
 end
 
 
-function final_retval(X, AX, resid_history, niter, n_matvec)
-    λ = real(diag(X' * AX))
-    residuals = AX .- X*Diagonal(λ)
-    (; λ, X,
-     residual_norms=[norm(residuals[:, i]) for i = 1:size(residuals, 2)],
+function final_retval(X, AX, BX, resid_history, niter, n_matvec)
+    λ = @views [(X[:, n]'*AX[:, n]) / (X[:, n]'BX[:, n]) for n=1:size(X, 2)]
+    λ = real(oftype(X[:, 1], λ))  # Offload to GPU if needed
+    residuals = AX .- BX .* λ'
+    if !issorted(λ)
+        p = sortperm(λ)
+        λ = λ[p]
+        residuals = residuals[:, p]
+        X = X[:, p]
+        AX = AX[:, p]
+        BX = BX[:, p]
+        resid_history = resid_history[p, :]
+    end
+    (; λ, X, AX, BX,
+     residual_norms=norm.(eachcol(residuals)),
      residual_history=resid_history[:, 1:niter+1], n_matvec)
 end
 
@@ -358,10 +368,11 @@ end
     nlocked = 0
     niter = 0  # the first iteration is fake
     λs = @views [(X[:, n]'*AX[:, n]) / (X[:, n]'BX[:, n]) for n=1:M]
-    λs = oftype(X[:, 1], λs)  # Offload to GPU if needed
+    λs = real(oftype(X[:, 1], λs))  # Offload to GPU if needed
     new_X = X
     new_AX = AX
     new_BX = BX
+    # The full_ arrays contain all the vectors, the others only get the active ones
     full_X = X
     full_AX = AX
     full_BX = BX
@@ -435,7 +446,7 @@ end
         if nlocked >= n_conv_check  # Converged!
             X .= new_X  # Update the part of X which is still active
             AX .= new_AX
-            return final_retval(full_X, full_AX, resid_history, niter, n_matvec)
+            return final_retval(full_X, full_AX, full_BX, resid_history, niter, n_matvec)
         end
         newly_locked = nlocked - prev_nlocked
         active = newly_locked+1:size(X,2)  # newly active vectors
@@ -524,5 +535,5 @@ end
         niter = niter + 1
     end
 
-    final_retval(full_X, full_AX, resid_history, maxiter, n_matvec)
+    final_retval(full_X, full_AX, full_BX, resid_history, maxiter, n_matvec)
 end