On the Determinants and Inverses of Circulant Matrices with Pell and Pell-Lucas Numbers
arXiv:1201.60616 citationsh-index: 9
Originality Synthesis-oriented
AI Analysis
Provides closed-form results for a specific class of structured matrices, but the contribution is incremental as it applies known techniques to a new number sequence.
The paper derives explicit formulas for determinants and inverses of circulant matrices whose entries are Pell and Pell-Lucas numbers, showing they are invertible for n≥3.
Let P=\circ(P_{1},P_{2},...,P_{n}) and Q=\circ(Q_{1},Q_{2},...,Q_{n}) be n\timesn circulant matrices where P_{n} and Q_{n} are nth Pell and Pell-Lucas numbers, respectively. The determinants of the matrices P and Q were expressed by the Pell and Pell-Lucas numbers. After, we prove that the matrices P and Q are the invertible for n\geq3 and then the inverses of the matrices P and Q are derived.