Positive-definite Kernel - Definition

Definition

Let

be a sequence of (complex) Hilbert spaces and

be the bounded operators from Hi to Hj.

A map A on where

is called a positive definite kernel if for all m > 0 and, the following positivity condition holds:

Read more about this topic:  Positive-definite Kernel

Famous quotes containing the word definition:

    ... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.
    George Eliot [Mary Ann (or Marian)

    Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.
    Elaine Heffner (20th century)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)