Unresolved issue

 

         The mathematical solution of the Neumann theorem, considered one of the most notorious open problems since their inception in the 30s of XX century by the Hungarian John von Neumann, will have "significant" for future generations applications, among others, medical scanner .
Eva Gallardo and Carl Cowen have an ending.

     "If you spin a ball, always swivels. Y are finite dimensional, where there is a subspace invariant for something that is a linear operator. Infinite in dimension, the problem was open," stated Gallardo after exposure Cowen, in English and using the motion of a basketball as an image. "What we've resolved," continued the professor, 39 years old and already produced several works on the U.S., "is that in infinite dimension, in a Hilbert space, there is always a subspace invariant, non-trivial, for any operator to be linear and continuous. "

The Hessian

The Hessian, which is also known as discriminant or Hessian matrix, was introduced in the year 1844 by Hesse, German mathematician, born in 1811 and dead in 1874. This Happened after that, Carl Gustav Jacob Jacobi introduce "The Jacobian".

The Hessian to determine the maximum and minimum of a function of two variables, also this one in optimization:

     - If the Hessian is positive, it is a minimum or maximum, depending on whether the second derivative of x is negative will be a maximum positive or if there is a minimum.

     

 -If the Hessian is negative, there will be a saddle point where there will be both maximum and minimum out of the same point.

     

 -If the Hessian is zero, we have enough information to determine anything, unless we see the full function drawn.