# Circulant decomposition of a matrix and the eigenvalues of Toeplitz type matrices

@article{Hariprasad2021CirculantDO, title={Circulant decomposition of a matrix and the eigenvalues of Toeplitz type matrices}, author={M. P. Hariprasad and Murugesan Venkatapathi}, journal={ArXiv}, year={2021}, volume={abs/2105.14805} }

. We begin by showing that any n ˆ n matrix can be decomposed into a sum of n circulant matrices with periodic relaxations on the unit circle. This decomposition is orthogonal with respect to a Frobenius inner product, allowing recursive iterations for these circulant components. It is also shown that the dominance of a few circulant components in the matrix allows sparse similarity transformations using Fast-Fourier-transform (FFT) operations. This enables the evaluation of all eigenvalues of…

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