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 ...

Some algorithms based upon a projection process onto the Krylov subspace $K_m = \operatorname{Span}(r_0, Ar_0, \ldots, A^{m - 1}r_0)$ are developed, generalizing the ...

Abstract: Recently, the notion of uniform observability with respect to a subspace was proposed in (Xia et al., 2022) and was utilized to solve the synchronization problem for single-integrator ...

As users have come to expect from Wolfram products, the Wolfram Linear Algebra Course Assistant is a wonderful resource for students of mathematics. Linear algebra is (unsurprisingly) the focus of ...

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 ...

Linearity, as first encountered in the algebra of vectors and matrices, provides the foundation for many other branches of mathematics. This course provides an introduction to two directions that ...