Guo's index for some classes of matrices

Robbiano, María

doi:10.1016/j.laa.2018.11.023

Cited by 2 publications

(3 citation statements)

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“…The spectra of certain classes of permutative matrices were studied in [17,18,23]. In particular, spectral results for matrices partitioned into symmetric blocks of order 2 were given.…”

Section: An Inverse Eigenvalue Problem For G-circulant Matricesmentioning

confidence: 99%

“…Suppose that g is a cyclic generator of U(Z/pZ). Let ϕ be the p − 1 primitive root of the unit defined as in (23). Consider the list given in (24) and let us define the auxiliary list…”

Section: Construction Of Nonnegative G-circulant Matrices Given Its Smentioning

confidence: 99%

“…Let p be a prime integer and consider g a cyclic generator of U(Z/pZ). Let ϕ as in (23). Given the set…”

mentioning

confidence: 99%

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On the spectra of some g-circulant matrices and applications to nonnegative inverse eigenvalue problem

Andrade

Arrieta

Manzaneda

et al. 2020

Linear Algebra and its Applications

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A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g−places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it is shown that spectra with sufficient conditions so that it can be the spectrum of a real g-circulant matrix is not a spectrum with sufficient conditions so that it can be the spectrum of a real circulant matrix of the same order. The obtained results are applied to Nonnegative Inverse Eigenvalue Problem to construct nonnegative, g-circulant matrices with given appropriated spectrum. Moreover, nonnegative g-circulant matrices by blocks are also studied and in this case, their orders can be a multiple of a prime number.

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“…The spectra of certain classes of permutative matrices were studied in [17,18,23]. In particular, spectral results for matrices partitioned into symmetric blocks of order 2 were given.…”

Section: An Inverse Eigenvalue Problem For G-circulant Matricesmentioning

confidence: 99%

“…Suppose that g is a cyclic generator of U(Z/pZ). Let ϕ be the p − 1 primitive root of the unit defined as in (23). Consider the list given in (24) and let us define the auxiliary list…”

Section: Construction Of Nonnegative G-circulant Matrices Given Its Smentioning

confidence: 99%