On Circulant Matrices

By I. Kra, Santiago R. Simanca. 2012

1,231 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c6a537a31ae14aa440d95239c20d84b17cd5c027

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Computations in quantum tensor networks (2012, background): “Being a sum (2) of Kronecker products of structured 2 × 2 matrices many Hamiltonians have special properties: they can be multilevel-circulant ([10, 11]) or skew-circulant, diagonal or persymmetric ([12]), which can be exploited to derive properties of the respective eigenvalues and eigenvectors.”
Deep Networks from the Principle of Rate Reduction (2020, background): “We refer the reader to Appendix B.1 or Kra & Simanca (2012) for properties of circulant matrices.”
Inference on Higher-Order Spatial Autoregressive Models with Increasingly Many Parameters (2015, neutral): “. Now define Win = ‖W ∗ in‖ −1W ∗in, (5.5) where ‖W ∗in‖ = η (W ∗ in) = 2i because W ∗ in is a symmetric, circulant matrix (see e.g. Davis (1979) p. 73), implying that (5.5) is row-normalisation.”
Practical Pulse-Shaping Waveforms for Reduced-Cyclic-Prefix OTFS (2019, background): “Let us first recall the following lemma on circulant matrices decomposition [13].”
The Structure of the Unit Group of the Group Algebra (2011, background): “For further details on circulant matrices, see Davis [6].”
An introduction to multivariate Krawtchouk polynomials and their applications (2013, background): “All of these examples have transition matrices for a single ball change which are circulants (Davis, 1979).”
Sparse Mixers: Combining MoE and Mixing to build a more efficient BERT (2022, methodology): “4 We compute the Fourier and Hartley transforms using the Fast Fourier Transform (FFT) (Coo-ley and Tukey, 1965; Frigo and Johnson, 2005).”
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials (2015, background): “[28]) All circulant matrices have the same ordered set of orthonormal eigenvectors {Xl}.”
Circulant Tensors with Applications to Spectral Hypergraph Theory and Stochastic Process (2013, background): “It is well-known [5, 9, 29] that the eigenvectors of C are given by vk = ( 1, ωk, ω 2 k, · · · , ωn−1 k )> , (4)”
Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains (2013, background): “they can be multilevel-circulant [4,6] or skew-circulant, diagonal or persymmetric [3], which can be exploited to derive properties of the respective eigenvalues and eigenvectors.”