On norms of principal submatrices

2021 ◽  
Author(s):  
F. Bünger ◽  
M. Lange ◽  
S.M. Rump
Keyword(s):  
Principal Submatrices

scholarly journals The almost semimonotone matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 291-303
Author(s):  
Megan Wendler
Keyword(s):  
Nonzero Vector ◽  
Principal Submatrix ◽  
Principal Submatrices

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.

On normal matrices with normal principal submatrices

1998 ◽  
Vol 89 (6) ◽  
pp. 1631-1651 ◽  
Author(s):  
Kh. D. Ikramov ◽  
L. Elsner
Keyword(s):  
Normal Matrices ◽  
Principal Submatrices
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