how to calculate the gradient of the matrix exponential function

[Poo Uoo]

Dear friends

I have a function expressed as: f(X) = Trace((e^{j*X})^H * A * e^{j*X)，

where X is a N*M phase matrix, A is a N*N matrix, H denote the conjugate transpose, and j^2=-1.

Anyone knows how to calculate the gradient w.r.t. X?

Thanks.

Poo

[Nicolas Boumal]

Hello,

You will need the differential of the matrix exponential, and possibly its adjoint.

See Manopt's dexpm function (also read help dexpm), and more info in Examples 4.26 and 4.29 of my book (free pdf online).

Best,

Nicolas