TITLE:
Classification of Computational Methods for High Powers of Matrices with Pedagogical Reflections
AUTHORS:
Xingjun Zhang
KEYWORDS:
High Powers of Matrices, Method Classification, Solution Selection Decision, Pedagogical Strategies
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.9,
September
17,
2026
ABSTRACT: The computation of high powers of matrices is a core component of linear algebra courses and a pervasive cognitive bottleneck for students. To address common teaching challenges such as fragmented methodological systems, the absence of systematic selection strategies, and frequent misapplication of underlying principles, this paper categorizes seven widely used computational methods into three modules: structural simplification, similarity transformation, and polynomial degree reduction. Their unified mathematical essence is revealed through the lenses of linear space decomposition and polynomial annihilation theory. A progressive decision flowchart is constructed based on the cost-based recommendation logic of computational operations, guiding students to select methods in ascending order of information acquisition cost. Furthermore, targeted teaching improvement strategies are proposed from three dimensions: thematic integration, condition discrimination, and integration of computational thinking, targeting four typical cognitive misconceptions.