scholarly journals The number of invariant polynomials of a matrix with prescribed complementary principal submatrices

1997 ◽  
Vol 251 ◽  
pp. 167-179 ◽  
Author(s):  
M. Graça^Marques ◽  
Fernando C. Silva ◽  
Zhang Yu Lin
2019 ◽  
Vol 7 (1) ◽  
pp. 291-303
Author(s):  
Megan Wendler

Abstract A (strictly) semimonotone matrix A ∈ ℝn×n is such that for every nonzero vector x ∈ ℝn with nonnegative entries, there is an index k such that xk > 0 and (Ax)k is nonnegative (positive). A matrix which is (strictly) semimonotone has the property that every principal submatrix is also (strictly) semimonotone. Thus, it becomes natural to examine the almost (strictly) semimonotone matrices which are those matrices which are not (strictly) semimonotone but whose proper principal submatrices are (strictly) semimonotone. We characterize the 2 × 2 and 3 × 3 almost (strictly) semimonotone matrices and describe many of their properties. Then we explore general almost (strictly) semimonotone matrices, including the problem of detection and construction. Finally, we relate (strict) central matrices to semimonotone matrices.


Sign in / Sign up

Export Citation Format

Share Document