The fractional Laplace transform corresponds to rotation by an arbitrary angle into the complex domain and can be represented by the matrix [ a b c d ] = [ i cos ⁡ ⁡ θ θ i sin ⁡ ⁡ θ θ i sin ⁡ ⁡ θ θ − − i cos ⁡ ⁡ θ θ ] . The Laplace transform is the fractional Laplace transform when θ θ = 90 ∘ ∘ . The inverse Laplace transform corresponds to θ θ = − − 90 ∘ ∘ .