Isomorphic Operators and Functional Equations for the Skew-Circulant Algebra

Abstract

The skew-circulant matrix has been used in solving ordinary differential equations. We prove that the set of skew-circulants with complex entries has an idempotent basis. On that basis, a skew-cyclic group of automorphisms and functional equations on the skew-circulant algebra is introduced. And different operators on linear vector space that are isomorphic to the algebra ofn×ncomplex skew-circulant matrices are displayed in this paper.

Gaussian Fibonacci Circulant Type Matrices

“…Abramyan proved the solvability of the system of (5) [8] for all ∈ , beginning with some 0 via that any circulant matrix is a normal matrix and its spectral norm is equal to the maximal modulus of its eigenvalues. Circulant type matrices have been put on the firm basis with the work in [9][10][11][12][13] and so on. There are discussions about the convergence in probability and in distribution of the spectral norm of circulant type matrices in [14].…”

Equalities and Inequalities for Norms of Block Imaginary Circulant Operator Matrices

“…The well-known circulant, block circulant-type matrices and operator norms have set up the strong basis with the work in [6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Explicit Determinants of the RFPrLrR Circulant and RLPrFrXu1, Jiang2, Jiang3 2014Abstract and Applied AnalysisSelf Cite1030View full textAdd to dashboardCite

“…They have been put on firm basis with the work of Davis [8] and Jiang and Zhou [9]. The circulant matrices, long a fruitful subject of research, have in recent years been extended in many directions [10][11][12][13]. The ( )-circulant matrices are another natural extension of this well-studied class and can be found in [14][15][16][17][18][19][20].…”