Showing papers on "Circulant matrix published in 1974"
TL;DR: In this paper, the spectral inverse of a Toeplitz matrix A whose form is related to that of a circulant matrix is studied by describing the algebraic structure of the semigroup of all matrices commuting with a given matrix with distinct eigenvalues.
109 citations
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract: © Publications mathématiques de l’I.H.É.S., 1974, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
20 citations
TL;DR: When n, r = 1, the Moore-Penrose pseudo-inverse of an $n \times n$r-circulant matrix is a strong spectral inverse.
Abstract: When $(n,r) = 1$, the Moore–Penrose pseudo-inverse of an $n \times n$r-circulant matrix is a strong spectral inverse.
2 citations
1 citations
01 Jan 1974
TL;DR: In this paper, the elements of the inverse of a circulant matrix having only 3 non-zero elements in each row (located in cyclically adjacent columns) are derived analytically from the solution of a recurrence equation.
Abstract: The elements of the inverse of a circulant matrix having only 3 non- zero elements in each row (located in cyclically adjacent columns) are de- rived analytically from the solution of a recurrence equation. Expressing any circulant as a product containing these 3-element type circulants then provides an algorithm for inverting circulants in general. Extension to generalized inverses of circulants whose row sum is zero is also made.