91 citations · 314 across the 15 of their papers we have counts for
15 papers
Positivity of a Hadamard Product
Roger A. Horn, Shengxuan Luo, Hongwei Xu +1
A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the facto…
Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence
Victor A. Bovdi, Roger A. Horn, Mohamed A. Salim +1
Let be a field of characteristic not , and let be a pair of matrices over , in which is symmetric and is skew-symmetric. A can…
Specht's criterion for systems of linear mappings
Vyacheslav Futorny, Roger A. Horn, Vladimir V. Sergeichuk
W.Specht (1940) proved that two complex matrices and are unitarily similar if and only if $\operatorname{trace} w(A,A^{\ast}) = \operatorname{trace} w(B,B^{\ast…
Representations of quivers and mixed graphs
Roger A. Horn, Vladimir V. Sergeichuk
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras…
Simultaneous unitary equivalences
Tatiana G. Gerasimova, Roger A. Horn, Vladimir V. Sergeichuk
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary m…
A canonical form for nonderogatory matrices under unitary similarity
Vyacheslav Futorny, Roger A. Horn, Vladimir V. Sergeichuk
A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms (i) for nonderogatory complex matrices up to unitary similarity and (ii) fo…