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 ...

An efficient computational algorithm is developed for solving linear matrix equations whose characteristic interaction matrix H' differs by a matrix of rank r from an interaction matrix H of a system ...

For systems of matrix equations of the form $$U' = A(t, U, V)V,\quad V' = - B(t, U, V)$$ it is shown here that the oscillation problem can be reduced to the ...

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 ...