Continuous Linear Extension
In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below. The resulting extension remains linear and bounded (thus continuous).
This procedure is known as continuous linear extension.
Read more about Continuous Linear Extension: Theorem, Application, The Hahn–Banach Theorem
Famous quotes containing the words continuous and/or extension:
“Perhaps when distant people on other planets pick up some wave-length of ours all they hear is a continuous scream.”
—Iris Murdoch (b. 1919)
“The motive of science was the extension of man, on all sides, into Nature, till his hands should touch the stars, his eyes see through the earth, his ears understand the language of beast and bird, and the sense of the wind; and, through his sympathy, heaven and earth should talk with him. But that is not our science.”
—Ralph Waldo Emerson (1803–1882)