The inverses of some circulant matrices

We present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover, we explicitly compute the inverse. Our study also encompasses a wide class of circulant symmetric matrices. The techniques we use are related with the so...

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Bibliographic Details
Published in:Applied mathematics and computation 2015-11, Vol.270, p.785-793
Main Authors: Carmona, A., Encinas, A.M., Gago, S., Jiménez, M.J., Mitjana, M.
Format: Article
Language:English
Subjects:
Chebyshev polynomials
Circulant matrix
Difference equations
Inverse matrix
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Summary:We present here necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and moreover, we explicitly compute the inverse. Our study also encompasses a wide class of circulant symmetric matrices. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. Consequently, we reduce the computational cost of the problem. In particular, we recover the inverses of some well known circulant matrices whose coefficients are arithmetic or geometric sequences, Horadam numbers among others. We also characterize when a general symmetric, circulant and tridiagonal matrix is invertible and in this case, we compute explicitly its inverse.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.08.084