diff --git a/src/precompile/factorizations.jl b/src/precompile/factorizations.jl
index 4b5793c1c..61c8ac120 100644
--- a/src/precompile/factorizations.jl
+++ b/src/precompile/factorizations.jl
@@ -26,13 +26,26 @@ function precompile_factorizations(::Type{S}; eltypes = PRECOMPILE_ELTYPES) wher
         t = randn(T, W ← W)            # square
         tr = randn(T, W ← V)           # tall (codomain larger) -> non-empty left null space
         tw = randn(T, V ← W)           # wide (domain larger)   -> non-empty right null space
-        th = (t + t') / 2              # hermitian (square, Euclidean inner product)
+
+        # projectors
+        th = project_hermitian(t)      # hermitian (square, Euclidean inner product)
+        project_antihermitian(t)
+        project_isometric(t)
+
+        # exponential
+        exponential(th)
 
         # Singular value decomposition
         svd_full(t)
         svd_compact(t)
         svd_vals(t)
         svd_trunc(t; trunc = truncrank(1))
+        svd_trunc(t; trunc = trunctol(; atol = 1.0e-10))
+        svd_trunc(t; trunc = truncerror(; atol = 1.0e-10))
+        svd_trunc(t; trunc = notrunc())
+        svd_trunc(t; trunc = truncspace(space(t, 1)))
+        svd_trunc(t; trunc = truncrank(1) | trunctol(; atol = 1.0e-10))
+        svd_trunc(t; trunc = truncrank(1) & trunctol(; atol = 1.0e-10))
 
         # QR / LQ decompositions (null-space variants on the appropriately shaped tensors)
         qr_full(t)
@@ -45,8 +58,22 @@ function precompile_factorizations(::Type{S}; eltypes = PRECOMPILE_ELTYPES) wher
         # Eigenvalue decompositions (hermitian variants require a hermitian input)
         eig_full(t)
         eig_vals(t)
+        eig_trunc(t; trunc = truncrank(1))
+        eig_trunc(t; trunc = trunctol(; atol = 1.0e-10))
+        eig_trunc(t; trunc = truncerror(; atol = 1.0e-10))
+        eig_trunc(t; trunc = notrunc())
+        eig_trunc(t; trunc = truncspace(space(t, 1)))
+        eig_trunc(t; trunc = truncrank(1) | trunctol(; atol = 1.0e-10))
+        eig_trunc(t; trunc = truncrank(1) & trunctol(; atol = 1.0e-10))
         eigh_full(th)
         eigh_vals(th)
+        eigh_trunc(th; trunc = truncrank(1))
+        eigh_trunc(th; trunc = trunctol(; atol = 1.0e-10))
+        eigh_trunc(th; trunc = truncerror(; atol = 1.0e-10))
+        eigh_trunc(th; trunc = notrunc())
+        eigh_trunc(th; trunc = truncspace(space(th, 1)))
+        eigh_trunc(th; trunc = truncrank(1) | trunctol(; atol = 1.0e-10))
+        eigh_trunc(th; trunc = truncrank(1) & trunctol(; atol = 1.0e-10))
 
         # Orthogonal / null-space helpers
         left_orth(t)