Derivatives, Gradients, Jacobians and Hessians

https://blog.demofox.org/2025/08/16/derivatives-gradients-jacobians-and-hessians-oh-my/

#HackerNews #Derivatives #Gradients #Jacobians #Hessians #MathExplained

The real vectorization vec(⋅) stacks the input columns into a vector. The Kronecker product ⊗ is related by vec(ABC) = (Cᵀ ⊗ B) vec(B).

We can similarly define a complex version vecc(⋅) = [vec(Re(⋅)); vec(Im(⋅))], with a corresponding #Kronecker product kroncc(⋅,⋅) such that vecc(ABC) = kroncc(Cᵀ, B) vecc(B).

Does anyone know of any literature that discusses the relevant properties of vecc and kroncc? They naturally appear when computing #Jacobians of functions of complex matrices.