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Invertible flexible matrices
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Abstract(s)
Matrices with coefficients having uncertainties of type o (.) or O(.), called flexible matrices, are studied from the point
of view of nonstandard analysis. The uncertainties of the afore-mentioned kind will be given in the form of the so-called neutrices,
for instance the set of all infinitesimals. Since flexible matrices have uncertainties in their coefficients, it is not possible to define
the identity matrix in an unique way and so the notion of spectral identity matrix arises. Not all nonsingular flexible matrices can
be turned into a spectral identity matrix using Gauss-Jordan elimination method, implying that that not all nonsingular flexible
matrices have the inverse matrix. Under certain conditions upon the size of the uncertainties appearing in a nonsingular flexible
matrix, a general theorem concerning the boundaries of its minors is presented which guarantees the existence of the inverse matrix
of a nonsingular flexible matrix.
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Citation
Justino, J. (2017). Invertible flexible matrices. AIP Conference Proceedings, 1836, 020071-1–020071-4. doi: 10.1063/1.4982011