A theorem on $M$-matrices and its extensions

V. L. Stefanyuk

Institute for Problems in Information Transmission, Academy of Sciences, USSR

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.

UDC: 512.8

Received: 10.06.1970

 English version: Mathematical Notes, 1973, 13:2, 141–148

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