期刊论文

Tsai, Ming-Cheng

英文

Linear Algebra and its Applications

0024-3795

2016

507

373-388

10.1016/j.laa.2016.06.023

The authors would like to thank Professors Man-Duen Choi, Chi-Kwong Li, Lajos Molnár, Tin-Yau Tam, and Ngai-Ching Wong for their useful comments. We are grateful for their important suggestions which helped to improve this paper. Liu was supported by the Taiwan MOST grant ( 104-2811-M-110-027 ). Szokol was supported by the “Lendület” Program ( LP2012-46/2012 ) of the Hungarian Academy of Sciences , by the Hungarian Scientific Research Fund (OTKA) Reg. No. K115383 and by a joint research project financed by HAS and the Ministry of Science and Technology , R.O.C. under the grant number 104-2911-I-110-508 .

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We show that if a map ϕon the set of positive definite matrices satisfiesdet⁡(A+B)=det⁡(ϕ(A)+ϕ(B)),ortr(AB−1)=tr(ϕ(A)ϕ(B)−1)with det⁡ϕ(I)=1, then ϕis of the form ϕ(A)=M⁎AM or ϕ(A)=M⁎AtM for some invertible matrix M with det⁡(M⁎M)=1. We also characterize the map ϕ:S→S preserving the similar trace equality or the determinant equalitydet⁡(tA+(1−t)B)=det⁡(tϕ(A)+(1−t)ϕ(B...