Abstract
In this paper we consider a useful condition for the positivity of the principal minors of a real matrix with nonnegative elements off the diagonal. This condition is useful for proving the convexity of certain sets in n-dimensional space, naturally connected with such matrices. Our result also yields a condition for the nonsingularity of a matrix with arbitrary (complex) elements, unifying conditions of Hadamard and Fidler.
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V. L. Stefanyuk and M. L. Tsetlin, “Regularizing the output of a collection of radio stations,” Problems in the Transmission of Information,3, No. 4 (1967), pp. 59–67.
F. R. Gantmacher, Theory of Matrices, Chelsea.
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Translated from Matematicheskii Zametki, Vol. 13, No. 2, pp. 235–246, February, 1973.
The author expresses his deep appreciation to N. N. Chentsov and S. V. Fomin for their valuable advice and remarks, used by the author in the preparation of this article.
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Stefanyuk, V.L. A theorem on M-matrices and its extensions. Mathematical Notes of the Academy of Sciences of the USSR 13, 141–148 (1973). https://doi.org/10.1007/BF01094232
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DOI: https://doi.org/10.1007/BF01094232