P-matrix, completion problem, combinatorial symmetry
An n-by-n real matrix is called a P-matrix if all its principal minors are positive. The P-matrix completion problem asks which partial P-matrices have a completion to a P-matrix. Here, we prove that every partial P-matrix with combinatorially symmetric specified entries has a P-matrix completion. The general case, in which the combinatorial symmetry assumption is relaxed, is also discussed.
Electronic Journal of Linear Algebra
Johnson, C. R., & Kroschel, B. K. (2014). The combinatorially symmetric P-matrix completion problem. Electronic Journal of Linear Algebra, 27(1). https://doi.org/10.13001/1081-3810.1004
This article was previously published in the Electronic Journal of Linear Algebra.