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February 21, 2026Annales Mathematicae Silesianae0 citationsOpen Access

On Powers, Roots and Moore–Penrose Inverses of Matrices Via Generalized Fibonacci Numbers

SKSinan KarakayaHÖHalim ÖzdemırAÖAhmet Yaşar Özban

Key Points

  • This research aims to explore the relationships between matrix powers, roots, and Moore–Penrose inverses in the context of generalized Fibonacci numbers.
  • Introduces new theoretical results regarding matrix properties.
  • Explores cubic matrix equations and their implications for various matrix types.
  • Provides numerical examples to validate theoretical findings.
  • Establishes connections between matrix inverses and Fibonacci sequences.
  • Demonstrates applicability to both square and rectangular matrices.

Abstract

Abstract The purpose of this work is to introduce some new results about the relations between powers, roots and Moore–Penrose inverses of square matrices satisfying a cubic matrix equation and the generalized Fibonacci numbers. The results can also be used for rectangular matrices. Moreover, we give some numerical examples to verify theoretical results.

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Cite This Study

Karakaya et al. (2026) studied this question.

synapsesocial.com/papers/69994c80873532290d021024https://doi.org/10.2478/amsil-2026-0002
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