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:

    I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.”
    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.”
    Jane Adams (20th century)