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:

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)

    Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.
    Nadine Gordimer (b. 1923)

    Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?
    Richard Eberhart (b. 1904)