Subtotally positive and Monge matrices

Miroslav Fiedler
2006 Linear Algebra and its Applications  
A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m × n matrix, only mn inequalities determine such class for every k, 1 k min(m, n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as
more » ... well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices.
doi:10.1016/j.laa.2005.08.020 fatcat:zwyetvro45asfjjzmwkkj5pus4