diff --git a/src/Picasso_BatchedLinearAlgebra.hpp b/src/Picasso_BatchedLinearAlgebra.hpp
index 7741f34..a18aa7c 100644
--- a/src/Picasso_BatchedLinearAlgebra.hpp
+++ b/src/Picasso_BatchedLinearAlgebra.hpp
@@ -12,6 +12,8 @@
 #ifndef PICASSO_BATCHEDLINEARALGEBRA_HPP
 #define PICASSO_BATCHEDLINEARALGEBRA_HPP
 
+#include <cassert>
+
 #include <Kokkos_Core.hpp>
 
 #include <functional>
@@ -1604,6 +1606,8 @@ struct Vector
 #pragma unroll
 #endif
         auto norm2 = Kokkos::sqrt( ~( *this ) * ( *this ) );
+        assert( norm2 != 0.0 );
+
         for ( int i = 0; i < N; ++i )
             ( *this )( i ) /= norm2;
         return *this;
@@ -1735,6 +1739,16 @@ struct Vector<T, 1>
         return *this;
     }
 
+    // Normalization
+    KOKKOS_INLINE_FUNCTION
+    Vector& normalize()
+    {
+        assert( ( *this )( 0 ) != 0.0 );
+
+        ( *this )( 0 ) = ( *this )( 0 ) > 0 ? 1.0 : -1.0;
+        return *this;
+    }
+
     // Strides.
     KOKKOS_INLINE_FUNCTION
     int stride_0() const { return 1; }
@@ -1898,6 +1912,8 @@ struct VectorView
 #pragma unroll
 #endif
         auto norm2 = Kokkos::sqrt( ~( *this ) * ( *this ) );
+        assert( norm2 != 0.0 );
+
         for ( int i = 0; i < N; ++i )
             ( *this )( i ) /= norm2;
         return *this;
diff --git a/unit_test/tstBatchedLinearAlgebra.hpp b/unit_test/tstBatchedLinearAlgebra.hpp
index e7277b0..73fd273 100644
--- a/unit_test/tstBatchedLinearAlgebra.hpp
+++ b/unit_test/tstBatchedLinearAlgebra.hpp
@@ -1128,6 +1128,11 @@ void vectorTest()
     for ( int i = 0; i < 3; ++i )
         EXPECT_DOUBLE_EQ( w( i ), 32.3 );
 
+    // Size 1 vector test
+    LinearAlgebra::Vector<double, 1> vec1 = { 4.7 };
+    vec1.normalize();
+    EXPECT_DOUBLE_EQ( vec1, 1.0 );
+
     // Size 1 vector test.
     // FIXME: construction of length 1 vector fails with NVCC.
     /*