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 ...

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title On the invariant subspace problem in Hilbert spaces. The paper is just 13 pages long and its ...

Math 307 is a theoretical course in linear algebra, geared primarily for students majoring in mathematics, mathematics and physics, and applied mathematics. (Although everyone is welcome, if you're ...

Given a vector space V of homogeneous polynomials of the same degree over an infinite field, consider a generic subspace W of V. The main result of this paper is a lower-bound (in general sharp) for ...