Oh shift !

In this neat video, I present the right and the left shift operators, and show some really neat and suprising facts about them! Hopefully by the end, this video will make you go "Oh shift!!!" Enjoy! :)

[qubix]

The title of this video is a great example of a case when pressing F for paying respects is critically necessary

[lars_]

Also R and L are adjoint with respect to the obvious scalar product when restricted to the subspace of square summable sequences.

[leonardromano]

For each linear transformation L:V->W over a field F there exists at least one l in F such that F(v)=l*v for some v in V.

[nadavslotky]

These are actually similar to known results in quantum mechanics, where the operators are equivalent to the raising and lowering operators (a-dagger and a) and the sequences are similar to superpositions of states of an harmonic oscillator

[shiina_mahiru_]

Here is what I see: Restrict the codomain of R and domain of L to the set of sequences begin with 0, then R and V gives an isomorphism. If we repeat the same thing with the set of sequence begin with two 0's, then three 0's, ... we will (mysteriously) obtain an infinite descending chain of isomorphic sets of sequences

[rogerkearns]

_Sia's sequence_
Sorry, you lost me. What's that all about? Thanks.