diff -r 102421d462d1 -r 53ab61a41d70 src/euclidean/wrap.rs
--- a/src/euclidean/wrap.rs	Wed Sep 03 21:03:47 2025 -0500
+++ b/src/euclidean/wrap.rs	Wed Sep 03 21:31:13 2025 -0500
@@ -135,6 +135,8 @@
         $crate::wrap!(impl_scalar_mut $F, $type, std::ops::MulAssign, mul_assign where $($qual)*);
         $crate::wrap!(impl_scalar_mut $F, $type, std::ops::DivAssign, div_assign where $($qual)*);
 
+        $crate::self_ownable!($type where $($qual)*);
+
         impl<$($qual)*> $crate::euclidean::Euclidean<$F> for $type
         // where
         //     Self: $crate::euclidean::wrap::Wrapped<WrappedField = $F>
@@ -153,6 +155,8 @@
         //         + for<'b> std::ops::SubAssign<&'b Self>
         //         + std::ops::Neg<Output = <Self as $crate::linops::AXPY>::Owned>,
         {
+            type PrincipalE = Self;
+
             fn dot<I: $crate::instance::Instance<Self>>(&self, other: I) -> $F {
                 other.eval_decompose(|x| self.get_view().dot(&x.get_view()))
             }
@@ -166,6 +170,22 @@
             }
         }
 
+        impl<$($qual)*> $crate::linops::VectorSpace for $type
+        // where
+        //     Self : $crate::euclidean::wrap::Wrapped<WrappedField = $F>,
+        //     Self::Unwrapped : $crate::linops::AXPY<Field = F>,
+        //     Self: std::ops::MulAssign<F> + std::ops::DivAssign<F>,
+        //     Self::Unwrapped: std::ops::MulAssign<F> + std::ops::DivAssign<F>,
+        {
+            type Field = $F;
+            type PrincipalV = Self;
+
+            /// Return a similar zero as `self`.
+            fn similar_origin(&self) -> Self::PrincipalV {
+                Self::wrap(self.get_view().similar_origin())
+            }
+        }
+
         impl<$($qual)*> $crate::linops::AXPY for $type
         // where
         //     Self : $crate::euclidean::wrap::Wrapped<WrappedField = $F>,
@@ -173,10 +193,7 @@
         //     Self: std::ops::MulAssign<F> + std::ops::DivAssign<F>,
         //     Self::Unwrapped: std::ops::MulAssign<F> + std::ops::DivAssign<F>,
         {
-            type Field = $F;
-            type Owned = Self;
-
-            fn axpy<I: $crate::instance::Instance<Self>>(&mut self, α: $F, x: I, β: $F) {
+             fn axpy<I: $crate::instance::Instance<Self>>(&mut self, α: $F, x: I, β: $F) {
                 x.eval_decompose(|v| {
                     self.get_view_mut().axpy(α, v.get_view(), β)
                 })
@@ -194,11 +211,6 @@
                 })
             }
 
-            /// Return a similar zero as `self`.
-            fn similar_origin(&self) -> Self::Owned {
-                Self::wrap(self.get_view().similar_origin())
-            }
-
             /// Set self to zero.
             fn set_zero(&mut self) {
                 self.get_mut_view().set_zero()
@@ -207,6 +219,7 @@
 
         impl<$($qual)*> $crate::instance::Space for $type {
             type Decomp = <<Self as $crate::euclidean::wrap::Wrapped>::Unwrapped as $crate::instance::Space>::Decomp;
+            type Principal = Self;
         }
     };
 }