diff -r 22fd33834ab7 -r d5dfcb6abcf5 src/direct_product.rs
--- a/src/direct_product.rs	Mon May 12 21:56:42 2025 -0500
+++ b/src/direct_product.rs	Mon May 12 22:48:16 2025 -0500
@@ -6,7 +6,9 @@
 */
 
 use crate::euclidean::Euclidean;
-use crate::instance::{Decomposition, DecompositionMut, Instance, InstanceMut, MyCow};
+use crate::instance::{
+    Decomposition, DecompositionMut, Instance, InstanceMut, Instantiated, MyCow,
+};
 use crate::linops::AXPY;
 use crate::loc::Loc;
 use crate::mapping::Space;
@@ -367,6 +369,25 @@
         Pair<A, B>: 'b;
 }
 
+impl<A, B, U, V, D, Q> Instantiated<Pair<A, B>, PairDecomposition<D, Q>> for Pair<U, V>
+where
+    A: Space,
+    B: Space,
+    U: Instantiated<A, D>,
+    V: Instantiated<B, Q>,
+    D: Decomposition<A>,
+    Q: Decomposition<B>,
+{
+    type RefInstance<'b>
+        = Pair<U::RefInstance<'b>, V::RefInstance<'b>>
+    where
+        Self: 'b;
+
+    fn ref_inst(&self) -> Self::RefInstance<'_> {
+        Pair(self.0.ref_inst(), self.1.ref_inst())
+    }
+}
+
 impl<A, B, U, V, D, Q> Instance<Pair<A, B>, PairDecomposition<D, Q>> for Pair<U, V>
 where
     A: Space,
@@ -376,6 +397,12 @@
     U: Instance<A, D>,
     V: Instance<B, Q>,
 {
+    type Instantiated = Pair<U::Instantiated, V::Instantiated>;
+
+    fn instantiate(self) -> Self::Instantiated {
+        Pair(self.0.instantiate(), self.1.instantiate())
+    }
+
     fn eval_decompose<'b, R>(
         self,
         f: impl FnOnce(Pair<D::Decomposition<'b>, Q::Decomposition<'b>>) -> R,
@@ -425,6 +452,14 @@
     &'a U: Instance<A, D>,
     &'a V: Instance<B, Q>,
 {
+    type Instantiated =
+        Pair<<&'a U as Instance<A, D>>::Instantiated, <&'a V as Instance<B, Q>>::Instantiated>;
+
+    fn instantiate(self) -> Self::Instantiated {
+        let &Pair(ref u, ref v) = self;
+        Pair(u.instantiate(), v.instantiate())
+    }
+
     fn eval_decompose<'b, R>(
         self,
         f: impl FnOnce(Pair<D::Decomposition<'b>, Q::Decomposition<'b>>) -> R,