diff --git a/benchmark/TensorAlgebraBenchmarks/TensorAlgebraBenchmarks.jl b/benchmark/TensorAlgebraBenchmarks/TensorAlgebraBenchmarks.jl
index d7974b2..9334a52 100644
--- a/benchmark/TensorAlgebraBenchmarks/TensorAlgebraBenchmarks.jl
+++ b/benchmark/TensorAlgebraBenchmarks/TensorAlgebraBenchmarks.jl
@@ -49,8 +49,8 @@ H = TensorValue(1.:81...)
 
 SUITE["Tensor algebra"]["δδ_μ_2d"] = @benchmarkable δᵢₖδⱼₗ2D + δᵢₗδⱼₖ2D
 SUITE["Tensor algebra"]["δδ_λ_2d"] = @benchmarkable 1.0 * δᵢⱼδₖₗ2D
-SUITE["Tensor algebra"]["Cofactor"] = @benchmarkable cof(A)
-SUITE["Tensor algebra"]["Det(A)Inv(A')"] = @benchmarkable det(A)*inv(A')
-SUITE["Tensor algebra"]["×ᵢ⁴"] = @benchmarkable ×ᵢ⁴(A)
-SUITE["Tensor algebra"]["IIsym"] = @benchmarkable IIsym(A)
-SUITE["Tensor algebra"]["push_forward_C_to_F"] = @benchmarkable push_forward_C_to_F(F,H)
+SUITE["Tensor algebra"]["Cofactor"] = @benchmarkable cof($A)
+SUITE["Tensor algebra"]["Det(A)Inv(A')"] = @benchmarkable det($A)*inv($A')
+SUITE["Tensor algebra"]["×ᵢ⁴"] = @benchmarkable ×ᵢ⁴($A)
+SUITE["Tensor algebra"]["IIsym"] = @benchmarkable IIsym($A)
+SUITE["Tensor algebra"]["push_forward_C_to_F"] = @benchmarkable push_forward_C_to_F($F,$H)
diff --git a/src/TensorAlgebra/Operations.jl b/src/TensorAlgebra/Operations.jl
index 24a974b..0f36f22 100644
--- a/src/TensorAlgebra/Operations.jl
+++ b/src/TensorAlgebra/Operations.jl
@@ -10,12 +10,26 @@ function (*)(Ten1::TensorValue, Ten2::TensorValue)
 end
 
 
-@inline @generated function (+)(A::TensorValue{D,D}, B::TensorValue{D,D}) where {D}
-  str = ""
-  for i in 1:D*D
-    str *= "A.data[$i] + B.data[$i], "
-  end
-  Meta.parse("TensorValue{D,D}($str)")
+# The element type is explicit so that empty tensors (e.g. `TensorValue{0,3}`,
+# built by Gridap for vertex grids) are also supported.
+@inline @generated function (+)(A::TensorValue{D1,D2}, B::TensorValue{D1,D2}) where {D1,D2}
+  T = promote_type(eltype(A), eltype(B))
+  data = [:(A.data[$i] + B.data[$i]) for i in 1:D1*D2]
+  :(TensorValue{D1,D2,$T}($(Expr(:tuple, data...))))
+end
+
+
+@inline @generated function (-)(A::TensorValue{D1,D2}, B::TensorValue{D1,D2}) where {D1,D2}
+  T = promote_type(eltype(A), eltype(B))
+  data = [:(A.data[$i] - B.data[$i]) for i in 1:D1*D2]
+  :(TensorValue{D1,D2,$T}($(Expr(:tuple, data...))))
+end
+
+
+@inline @generated function (-)(A::TensorValue{D1,D2}) where {D1,D2}
+  T = eltype(A)
+  data = [:(-A.data[$i]) for i in 1:D1*D2]
+  :(TensorValue{D1,D2,$T}($(Expr(:tuple, data...))))
 end
 
 
diff --git a/src/TensorAlgebra/TensorAlgebra.jl b/src/TensorAlgebra/TensorAlgebra.jl
index dfc7839..76abf9a 100644
--- a/src/TensorAlgebra/TensorAlgebra.jl
+++ b/src/TensorAlgebra/TensorAlgebra.jl
@@ -6,9 +6,11 @@ using StaticArrays
 using LinearAlgebra
 import Base: *
 import Base: +
+import Base: -
 
 export (*)
 export (+)
+export (-)
 export (⊗₁₂³)
 export (⊗₁₃²)
 export (⊗₁²³)
diff --git a/test/TestTensorAlgebra/TensorAlgebraTests.jl b/test/TestTensorAlgebra/TensorAlgebraTests.jl
index 8b34bad..d99e96d 100644
--- a/test/TestTensorAlgebra/TensorAlgebraTests.jl
+++ b/test/TestTensorAlgebra/TensorAlgebraTests.jl
@@ -107,6 +107,15 @@ end
   B = TensorValue(4.1, 5.2, 6.3, 7.4, 8.5, 9.6, 1.7, 2.8, 3.9)
   @test A + B == TensorValue(5.1, 7.2, 9.3, 11.4, 13.5, 15.6, 8.7, 10.8, 12.9)
   @test norm(A + B) ≈ 32.842807431765024
+  @test B - A ≈ TensorValue(3.1, 3.2, 3.3, 3.4, 3.5, 3.6, -5.3, -5.2, -5.1)
+  @test -A == TensorValue(-1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0, -8.0, -9.0)
+  C = TensorValue{2,3}(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+  @test C + C == TensorValue{2,3}(2.0, 4.0, 6.0, 8.0, 10.0, 12.0)
+  @test TensorValue{2,2}(1, 2, 3, 4) + TensorValue{2,2}(0.5, 0.5, 0.5, 0.5) isa TensorValue{2,2,Float64}
+  E = TensorValue{0,3,Float64}(())  # empty tensor, built by Gridap for vertex grids
+  @test E + E == E
+  @test E - E == E
+  @test -E == E
 end