Ranks of Hermitian and skew-Hermitian solutions to the matrix equation AXA∗=B
- Liu, Yonghui
- Tian, Yongge
- Takane, Yoshio
DOIAbstract
AbstractGiven a complex matrix equation AXA∗=B, where B∗=±B, we present explicit formulas for the maximal and minimal ranks of Hermitian (skew-Hermitian) solutions X to the equation as well as the maximal and minimal ranks of the real matrices X0 and X1 in a Hermitian (skew-Hermitian) solution X=X0+iX1. As applications, we give the maximal and minimal ranks of the real matrices C and D in a Hermitian (skew-Hermitian) g-inverse (A+iB)-=C+iD of a Hermitian (skew-Hermitian) matrix A+iB
Add to ORKG