Different Bounds of Various Norms of Special Matrices with Generalized Pell–Lucas Sequence

Norm bounds for circulant-type matrices associated with the bi-periodic Pell–Lucas sequence are examined from a symmetry-driven perspective. By incorporating alternating recurrence coefficients, the results clarify how periodicity and circulant structure affect spectral norm behavior through explicit bounds. This framework extends existing Pell–Lucas-type matrix inequalities and emphasizes the role of symmetry in spectral analysis.