Estimates of the p-Norms of Solutions and Inverse Matrices of Systems of Linear Equations with a Circulant Matrix

The article considers the problem of estimating solutions and inverse matrices of systems of linear equations with a circulant matrix in the \(p\) -norm, \(1 \leqslant p < \infty \) . An estimate for a diagonally dominant circulant matrix is obtained. Based on this result and the idea of decomposing a matrix into a product of matrices associated with the decomposition of a characteristic polynomial, an estimate for the general circulant matrix is proposed.