Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

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 ...

Random matrix theory (RMT) has emerged as a powerful framework for analysing complex systems across physics, statistics and beyond, by examining the statistical properties of matrices with random ...

To learn math, students must build a mental toolbox of facts and procedures needed for different problems. But students who can recall these foundational facts in isolation often struggle to use them ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...