The infinite-dimensional space P of all finite-degree polynomials gives a memorable example of the non-commutativity of linear maps. Let d/dx: P †’ P be the usual derivative and let s: P †’ P be the shift map.

Show that the two maps don't commute d/dx —¦ s ‰  s —¦ d/dx, in fact, not only is
(d/dx —¦ s) - (s —¦ d/dx) not the zero map, it is the identity map.

Transcribed Image Text:

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