Row cones, perron similarities, and nonnegative spectra. Issue 10 (3rd October 2017)

• Record Type: Journal Article
• Authors: Johnson, Charles R.; Paparella, Pietro
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 10(2017)
• Page Start: 2124
• Page End: 2130
• Publication Date: 2017-10-03
• Subjects: Perron similarity -- row hadamard conic -- real non-negative inverse eigenvalue problem -- Hadamard product -- row cone -- spectracone; Primary: 15A18 -- 15A29 -- 15B48; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1329269
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: In further pursuit of the diagonalizable real nonnegative inverse eigenvalue problem (RNIEP), we study the relationship between the row cone and the spectracone of a Perron similarity S . In the process, a new kind of matrix, row Hadamard conic (RHC), is defined and related to the D-RNIEP. Characterizations are given when, and explicit examples are given for all possible set-theoretic relationships between the two cones. The symmetric NIEP is the special case of the D-RNIEP in which the Perron similarity S is also orthogonal.