complex Hessian matrix
Suppose that be twice differentiable and let
Then the is the matrix
When applied to tangent vectors of the zero set of , it is called the Levi form and used to define a Levi pseudoconvex point of a boundary of a domain. Note that the matrix is not the same as the (real) Hessian. A twice continuously differentiable real valued function with a positive semidefinite real Hessian matrix at every point is convex, but a function with positive semidefinite matrix at every point is plurisubharmonic (since it’s continuous it’s also called a pseudoconvex function).
- 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Title||complex Hessian matrix|
|Date of creation||2013-03-22 14:31:16|
|Last modified on||2013-03-22 14:31:16|
|Last modified by||jirka (4157)|