just take second derivatives the way you took first ones, and write the Hessian as the 2x2 matrix each entry of which is also a matrix (I guess it can be viewed as a tensor if needed)
I have got the following function constructed by matrices and vectors:
in which, are vectors. are matrices.
The gradients with respect to are:
in which, is the transpose of and is the first order derivative of .
Anyone knows how to get the Hessian of the ? Thanks a lot!
Thanks a lot! But could you please tell me more details? I guess it should be:
because the Hessian should be symmetric, am I right?
Moreover, due to the equation:
then the second order partial derivative:
will involve . I do not know if I am correct. Please show me the analytic form of the Hessian. Thank you very much!
By the way, may I ask you another related question please?
I want to know the relations between 'Gradient', 'Jacobian' and 'Hessian'. What I think they are:
'Function':
'Gradient':
'Jacobian' :
'Hessian':
Am I right? Are there any definition for these relations please? Thanks very much!
no, those relations are just wrong
Gradient - Wikipedia, the free encyclopedia
Hessian matrix - Wikipedia, the free encyclopedia
Jacobian - Wikipedia, the free encyclopedia