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MATRIX IDENTITIES INVOLVING POWER SUMS AND STRUCTURED SEQUENCES
Keywords:
matrix identities, matrix powers, Fibonacci sequence, Lucas sequenceDOI:
https://doi.org/10.17654/0972087125033Abstract
This paper presents new matrix identities involving powers and products of structured matrices whose entries are derived from real-valued sequences. These identities reveal deep algebraic relationships among matrix powers and products, leading to closed-form expressions for classical number-theoretic sequences. Applications to the Fibonacci and Lucas sequences are discussed, and a generalization involving power-sum matrices is introduced. The results highlight the effectiveness of matrix-based techniques in deriving elegant and compact representations of linear recurrence sequences.
Received: June 20, 2025
Accepted: July 21, 2025
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