Nonsingularity criteria for matrices involving combinatorial considerations
In this survey paper several related combinatorially-based singularity criteria for matrices over arbitrary fields are surveyed. The best way to express the focus of the paper is to list titles of the sections: 1. Introduction; elementary criteria for matrices over arbitrary fields; 2. L-matrices (sign nonsingularity); 3. Potential nonsingularity and complete matchings; 4. Stable nonsingularity; 5. Closed sets in graphs; 6. Another undirected graph of a matrix; acyclic matrices; 7. A nonsingularity criterion for irreducible acyclic matrices with zero diagonal; 8. A nonsingularity criterion for general combinatorially symmetric matrices. The results in last two paragraphs are taken from [\textit{D. Carlson} and \textit{D. Hershkowitz}, Nonsingularity criteria for general combinatorially symmetric matrices, Linear Algebra Appl. 114/115, 399-416 (1989; see the review above)].
scientific article; zbMATH DE number 4123772