Some results on symmetric circulant matrices and on symmetric centrosymmetric matrices

By Oscar Rojo, Héctor Rojo. 2004

64 citations recorded by the source corpus.

We derive a readily computable sufficient condition for the existence of a nonnegative symmetric circulant matrix having a prescribed spectrum. Moreover, we prove that any set λ1 ⩾ λ2 ⩾ ⋯ ⩾ λn is the spectrum of real symmetric centrosymmetric matrices S1 and S2 such that for S1 an eigenvector corresponding to λ1 is the all ones vector and for S2 an eigenvector corresponding to λ1 is the vector with components 1 and −1 alternately. The proof is constructive. Then, we derive an improved condition on {λk}k=1n such that S1 = λ1E, where E is a stochastic symmetric centrosymmetric matrix. Finally, we propose an algorithm to compute the eigenvalues of some real symmetric centrosymmetric matrices. All the numerical procedures are based on the use of the Fast Fourier Transform.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8566c0c01aeb0ecace6f183638fef2b151086e56

Citations in the corpus

• Infrared Dim and Small Target Detection via Multiple Subspace Learning and Spatial-Temporal Patch-Tensor Model (2021, unknown): “Besides, Ā (i) has an interesting property [50] ⎧⎨ ⎩ Ā (1) ∈ n1×n2”