Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598571 | Linear Algebra and its Applications | 2016 | 16 Pages |
Abstract
We show that if a map ϕ on the set of positive definite matrices satisfiesdet(A+B)=det(ϕ(A)+ϕ(B)),ortr(AB−1)=tr(ϕ(A)ϕ(B)−1)with detϕ(I)=1, then ϕ is of the form ϕ(A)=M⁎AMϕ(A)=M⁎AM or ϕ(A)=M⁎AtMϕ(A)=M⁎AtM for some invertible matrix M with det(M⁎M)=1det(M⁎M)=1. We also characterize the map ϕ:S→Sϕ:S→S preserving the similar trace equality or the determinant equalitydet(tA+(1−t)B)=det(tϕ(A)+(1−t)ϕ(B)),t∈[0,1],in SS, where SS denotes the set of complex matrices, symmetric matrices, or upper triangular matrices, respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Huajun Huang, Chih-Neng Liu, Patrícia Szokol, Ming-Cheng Tsai, Jun Zhang,