Abstract
The property of a Hermitian n × n matrix A that all its principal minors of order n − 1 vanish is shown to be a purely algebraic implication of the fact that the lowest two coefficients of its characteristic polynomial are zero. To prove this assertion, no information on the rank or eigenvalues of A is required.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 47–49.
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Ikramov, K.D. On the principal minors of a matrix with a multiple eigenvalue. J Math Sci 137, 4787–4788 (2006). https://doi.org/10.1007/s10958-006-0276-6
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DOI: https://doi.org/10.1007/s10958-006-0276-6