Eigenvalue problem phase 1: $\boldsymbol{A}\rightarrow \boldsymbol{H},,\left( \boldsymbol{A}\sim \boldsymbol{H} \right)$, $\boldsymbol{H}$ is a upper Hessenberg ...
ABSTRACT: This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of ...
This paper takes another look at the convergence analysis of the Arnoldi procedure for solving non-Hermitian eigenvalue problems. Two main viewpoints are put in contrast. The first exploits the ...
“Mathematics is the art of reducing any problem to linear algebra.” This is a quote often attributed to William Stein, a former mathematics professor at the University of Washington, now the lead ...
The teaching and learning of linear algebra have evolved significantly over recent decades, underpinned by diverse approaches ranging from theoretical expositions to dynamic, model-based environments.
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