diff --git a/docs/src/algebra.md b/docs/src/algebra.md
index 21af34f..0360c10 100644
--- a/docs/src/algebra.md
+++ b/docs/src/algebra.md
@@ -342,7 +342,7 @@ These methods can be applied to any `MultiVector` simplicial complex.
 Let ``v_\pm^2 = \pm1`` be a basis with ``v_\infty = v_++v_-`` and ``v_\emptyset = (v_--v_+)/2``
 An embedding space ``\mathbb R^{p+1,q+1}`` carrying the action from the group ``O(p+1,q+1)`` then has
 ``v_\infty^2 =0``, ``v_\emptyset^2 =0``,
-``v_\infty \cdot v_\emptyset = 1``,  and ``v_{\infty\emptyset}^2 = 1`` with
+``v_\infty \cdot v_\emptyset = -1``,  and ``v_{\infty\emptyset}^2 = 1`` with
 Minkowski plane ``v_{\infty\emptyset}`` having the Hestenes-Dirac-Clifford product properties,
 ```@repl ga
 using Grassmann; @basis S"∞∅++"
diff --git a/src/composite.jl b/src/composite.jl
index 5fcc660..9053990 100644
--- a/src/composite.jl
+++ b/src/composite.jl
@@ -57,10 +57,12 @@ end
 @inline unabs!(t::Expr) = (t.head == :call && t.args[1] == :abs) ? t.args[2] : t
 
 function Base.exp(t::T) where T<:TensorGraded
-    S = T<:SubManifold
-    i = T<:TensorTerm ? basis(t) : t
+    S,B = T<:SubManifold,T<:TensorTerm
+    i = B ? basis(t) : t
     sq = i*i
-    if isscalar(sq)
+    if B && isnull(t)
+        return one(V)
+    elseif isscalar(sq)
         hint = value(scalar(sq))
         isnull(hint) && (return 1+t)
         grade(t)==0 && (return Simplex{Manifold(t)}(AbstractTensors.exp(value(S ? t : scalar(t)))))
diff --git a/src/multivectors.jl b/src/multivectors.jl
index e74842e..e10e11d 100644
--- a/src/multivectors.jl
+++ b/src/multivectors.jl
@@ -63,6 +63,11 @@ function (m::Chain{V,G,T})(i::Integer) where {V,G,T}
     Simplex{V,G,SubManifold{V}(indexbasis(ndims(V),G)[i]),T}(m[i])
 end
 
+Chain{V,1}(m::SMatrix{N,N}) where {V,N} = Chain{V,1}(Chain{V,1}.(getindex.(Ref(m),:,SVector{N}(1:N))))
+Chain{V,1,Chain{W,1}}(m::SMatrix{M,N}) where {V,W,M,N} = Chain{V,1}(Chain{W,1}.(getindex.(Ref(m),:,SVector{N}(1:N))))
+
+Base.inv(m::Chain{V,1,<:Chain{W,1}}) where {V,W} = Chain{V,1,Chain{W,1}}(inv(SMatrix(m)))
+
 function show(io::IO, m::Chain{V,G,T}) where {V,G,T}
     ib = indexbasis(ndims(V),G)
     @inbounds tmv = typeof(m.v[1])
@@ -123,7 +128,9 @@ function clearbundlecache!()
 end
 @pure bundle(::ChainBundle{V,G,T,P} where {V,G,T}) where P = P
 @pure deletebundle!(V) = deletebundle!(bundle(V))
-@pure deletebundle!(P::Int) = (bundle_cache[P] = [Chain{ℝ^0,0,Int}(SVector(0))])
+@pure function deletebundle!(P::Int)
+    bundle_cache[P] = [Chain{ℝ^0,0,Int}(SVector(0))]
+end
 @pure isbundle(::ChainBundle) = true
 @pure isbundle(t) = false
 @pure ispoints(t) = isbundle(t) && rank(t) == 1 && !isbundle(Manifold(t))