On a type of circulants
TLDR
In this paper, the eigenvalues of many retrocirculants were determined and a necessary and sufficient condition for a permutation matrix to commute with a retrocircular matrix was presented.About:
This article is published in Linear Algebra and its Applications.The article was published on 1973-01-01 and is currently open access. It has received 11 citations till now. The article focuses on the topics: Generalized permutation matrix & Permutation matrix.read more
Citations
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The isomorphism problem for circulant graphs via Schur ring theory.
TL;DR: The developed machinery allows us to give proofs of two eonjectures about necessary conditions on isomorphisms of the cireulants, which show the feasibility of the teehnique of Schur rings in algebraic combinatorics.
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Generalized inverses of circulant and generalized circulant matrices
C.Leary Bell,C.Leary Bell +1 more
TL;DR: In this paper, an expression for the Moore-Penrose inverse of certain singular circulants by S.R. Searle is generalized to include all circulant blocks, and expressions for other generalized inverses are given.
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Norm equalities and inequalities for three circulant operator matrices
TL;DR: In this paper, the scaling circulant operator matrices, diag-circulant matrices and retrocircular matrices are shown to have norm equalities and inequalities, and a pinching type inequality is given for weakly unitarily invariant norms.
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The Moore-Penrose inverse of a retrocirculant
TL;DR: In this article, the Moore-Penrose inverse of such a "retrocirculant" was determined and the nonzero eigenvalues of the inverse were the reciprocals of the non zero eigen values of the retrocirculant.
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On the generalization of a retrocirculant
TL;DR: In this article, the properties of matrices of the form P (σ) A where σ is induced by an automorphism of an abelian group G and A is a group matrix were studied.
References
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Two Notes on Matrices
TL;DR: The circulant matrix C of order 4 x 4, with elements in the complex field, was shown to be a reducible matrix representation of the cyclic group ℐ 4, and C is a group matrix for this as discussed by the authors.