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

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