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The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different but closely related things.. Pushforward (differential), the differential of a smooth map between manifolds, and the "pushforward" operations it defines
Let : be a smooth map of smooth manifolds. Given , the differential of at is a linear map : from the tangent space of at to the tangent space of at (). The image of a tangent vector under is sometimes called the pushforward of by .
In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.
The following is an alphabetical list of Greek and Latin roots, stems, and prefixes commonly used in the English language from P to Z. See also the lists from A to G and from H to O.
Fobbie or Fobbit – A Marine who rarely sees combat; pejorative term for Marines stuck inside a forward operating base. Follow it – Said when a rifle is dropped by a Marine, the Marine is expected to follow it to the ground by doing a push up as punishment for allowing their rifle to hit the deck. Also used when a Marine drops anything.
By the end of last week the president and his team had settled on a strategy forward, the five people familiar with the internal discussions said. That strategy, as described by multiple Biden ...
Problems. Vector fields don't push forward, for one thing. The pushforward of a vector field only exists under some conditions on F, which are expressed generally in terms of DF. So that's all a bit circular. This can be mentioned, but not as a definition: tangent vectors do push forward individually, and the curve approach to seeing that is fine.
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