diff --git a/src/tensors/linalg.jl b/src/tensors/linalg.jl
index 40a0e0024..f07f1b174 100644
--- a/src/tensors/linalg.jl
+++ b/src/tensors/linalg.jl
@@ -421,7 +421,23 @@ function exp!(t::TensorMap)
     domain(t) == codomain(t) ||
         error("Exponential of a tensor only exist when domain == codomain.")
     for (c, b) in blocks(t)
-        copy!(b, LinearAlgebra.exp!(b))
+        MatrixAlgebraKit.exponential!(b, b)
+    end
+    return t
+end
+
+function exp!((τ, t)::Tuple{Number, TensorMap})
+    domain(t) == codomain(t) ||
+        error("Exponential of a tensor only exist when domain == codomain.")
+    if eltype(t) <: Real && eltype(τ) <: Complex
+        t_complex = complex(t)
+        for ((cr, br), (cc, bc)) in zip(blocks(t), blocks(t_complex))
+            MatrixAlgebraKit.exponential!((τ, br), bc)
+        end
+        return t_complex
+    end
+    for (c, b) in blocks(t)
+        MatrixAlgebraKit.exponential!((τ, b), b)
     end
     return t
 end
diff --git a/test/tensors/exponential.jl b/test/tensors/exponential.jl
new file mode 100644
index 000000000..51fe1072b
--- /dev/null
+++ b/test/tensors/exponential.jl
@@ -0,0 +1,25 @@
+using Test, TestExtras
+using TensorKit
+using Random
+
+spaces = [ℂ^4, Vect[U1Irrep](0 => 1, 1 => 2), Vect[SU2Irrep](0 => 1, 1 // 2 => 1)]
+scalartypes = [Float64, ComplexF64]
+
+@timedtestset "exp!(τ,A) for $space, scalartype(A) = $st1, scalartype(τ) = $st2" for space in spaces, st1 in scalartypes, st2 in scalartypes
+    A = randn(st1, space, space)
+    τ = rand(st2)
+
+    @test exp!(copy(A)) == exp!((1.0, copy(A)))
+
+    A2 = exp!((τ, A))
+    if st1 <: Real && st2 <: Complex
+        @test objectid(A2) != objectid(A)
+    else
+        @test objectid(A2) == objectid(A)
+    end
+
+    expτA = exp!((τ, copy(A)))
+    expminτA = exp!((-τ, copy(A)))
+    @test expτA * expminτA ≈ id(scalartype(expτA), space)
+    @test expτA ≈ inv(expminτA)
+end