2023/06/17 by Patrick Otto Ludl, Ludl, Patrick Otto
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2306.10415
openalex publication_date 2023/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are equally suited to unravel properties of the problem to be solved. In this paper a normal form for bases of finite-dimensional vector spaces is introduced which may prove very useful in the context of understanding the structure of the problem in which the basis appears in a step towards the solution. This normal form may be viewed as a new normal form for matrices of full column rank.