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 ...

Abstract: Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding ...

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 ...

Homogeneity: T(c * u) = c * T(u) for any scalar c and vector u. Additivity: T(u + v) = T(u) + T(v) for any vectors u and v. The range of a linear transformation T is the set of all vectors that can be ...

Let F be a complex Banach space, B(F) the algebra of all bounded operators acting on F, E = E(ℂ, B(F)) the Fréchet space of all entire functions from the complex plane into B(F), endowed with the ...

Abstract: In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least ...

This repository contains the linear algbra chapter that I wrote for the upcoming book "Python Jupyter Notebooks for College Math Teachers." The book is currently undergoing editing, but we expect a ...