Expanders – Lecture 3 – Part 2 – YouTube


http://m.youtube.com/?reload=9&rdm=mn4dxd2xg#/watch?v=cbYcn8o0Jfg&feature=player_embedded&desktop_uri=%2Fwatch%3Fv%3DcbYcn8o0Jfg%26feature%3Dplayer_embedded

Luca explains why the power method works, as an algorithm. In the course he explains the concepts behind tge steps – which are really quite intuitive (once you recognize what certain symbols are modelling). In particular one sees reasoning about orthogonal eigenspaces, preserved by the numerical method.

While its fun to see this explained in matrix centric theory (taught to every 14 year old since 1950), its even more fun too see the same argument made in pure group theory. Orthogonality in 1920s relativity math is more about permutation cycle lengths, letting a cycle (term) act as a generator (in a cayley graph), cycle closure, and self-conjygate subgroups of the symmetric group. Eigenvalues are addressed more geometrically, than in special linear groups. A series of 2k+1 matrix multiples may look more like conjugation of a cycle by a 2k+1 (or 2mk+1, rather) term

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