We study the following question: suppose that A and ℬ are two algebras of complex n × n matrices such that the ring commutator [A, B] = AB – BA is "small" for each A ∈ A and B ∈ ℬ; does this imply ...

This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

Gravitational lensing often evokes images of a cosmic funhouse mirror: duplicated galaxies, dramatic arcs and distorted shapes. But the web-like, large-scale structure throughout the universe also ...