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Determinant evaluations for binary circulant matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Determinant formulas for special binary circulant matrices are derived and a new open problem regarding the possible determinant values of these specific circulant matrices is stated. The ideas used for the proofs can be utilized to obtain more determinant formulas for other binary circulant matrices, too. The superiority of the proposed approach over the standard method for calculating the determinant of a general circulant matrix is demonstrated.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-05-28
zaakceptowano
2014-11-13
online
2014-12-09
Twórcy
  • Department of Mathematics, University of Athens, Panepistimiopolis 15784,
    Athens, Greece
Bibliografia
  • [1] J. Bae. Circulant Matrix Factorization Based on Schur Algorithm for Designing Optical Multimirror Filters. Japan. J. Math.45:5163–5168, 2006.
  • [2] R. A. Brualdi and H. Schneider. Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace,Muir and Cayley. Linear Algebra Appl. 52:769–791, 1983.[WoS]
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  • [4] S. Georgiou and C. Kravvaritis. New Good Quasi-Cyclic Codes over GF(3). Int. J. Algebra 1:11–24, 2007.
  • [5] R. M. Gray. Toeplitz and Circulant Matrices: A review. Found. Trends Comm. Inform. Theory 2:155–239, 2006.
  • [6] F. A. Graybill. Matrices with applications in statistics. Prentice Hall, Wadsworth-Belmont, 1983.
  • [7] K. Grifln and M. J. Tsatsomeros. Principal minors, Part I: A method for computing all the principal minors of amatrix. LinearAlgebra Appl. 419:107–124, 2006.
  • [8] K. J. Horadam. Hadamard matrices and their applications. Princeton University Press, Princeton and Oxford, 2007.
  • [9] R. A. Horn and C. R. Johnson. Matrix Analysis. Cambridge University Press, Cambridge, 1985.
  • [10] T. K. Huckle. Compact Fourier Analysis for Designing Multigrid Methods. SIAM J. Comput. 31:644–666, 2008.[WoS]
  • [11] T. K. Huckle and C. Kravvaritis, Compact Fourier Analysis for Multigrid Methods based on Block Symbols, SIAM J. MatrixAnal. Appl., 33:73–96, 2012.[WoS]
  • [12] C. Koukouvinos, M. Mitrouli and J. Seberry.Growth in Gaussian elimination for weighingmatrices,W(n, n−1). Linear AlgebraAppl. 306:189–202, 2000.
  • [13] C. Koukouvinos, M. Mitrouli and J. Seberry. An algorithm to find formulae and values of minors for Hadamard matrices.Linear Algebra Appl., 330:129–147, 2001.
  • [14] S. Kounias, C. Koukouvinos, N. Nikolaou and A. Kakos. The nonequivalent circulant D-optimal designs for n ≡ 2mod 4, n =54, n = 66. J. Combin. Theory Ser. A 65:26–38, 1994.
  • [15] C. Krattenthaler. Advanced determinant calculus. Sém. Lothar. Combin. 42:69–157, 1999.
  • [16] C. Krattenthaler. Advanced determinant calculus: A complement. Linear Algebra Appl., 411:68–166, 2005.
  • [17] G. Maze and H. Parlier. Determinants of Binary Circulant matrices. IEEE Trans. Inform. Theory p. 124, 2004.
  • [18] A. R. Moghaddamfar, S. M. H. Pooya, S. Navid Salehy and S. Nima Salehy. More calculations on determinant evaluations.Electron. J. Linear Algebra 16:19–29, 2007.
  • [19] N. Nguyen, P. Milanfar and G. Golub. A Computationally Eflcient Superresolution Image Reconstruction Algorithm. IEEETrans. Image Process. 10:573–583, 2001.[Crossref][PubMed]
  • [20] J. Seberry, T. Xia, C. Koukouvinos and M. Mitrouli. The maximal determinant and subdeterminants of ±1 matrices. LinearAlgebra Appl. 373:297–310, 2003.[WoS]
  • [21] F. R. Sharpe. The maximum value of a determinant. Bull. Amer. Math. Soc. 14:121–123, 1907.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2014-0019
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