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 ...

Analog computers are systems that perform computations by manipulating physical quantities such as electrical current, that map math variables, instead of representing information using abstraction ...

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 ...

Computer scientists have devised an innovative and elegantly concise algorithm that can efficiently solve systems of linear equations that are critical to such important computer applications as image ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

The class of second-order linear dynamical systems is considered. A method and algorithm are presented to transform any system with n degrees of freedom into n independent second-order equations. The ...

My understanding of linear independance is that if you have a unique solution after rref, it's linear independant. If you have multiple solutions or no solution, it's not linear ...