Xuân Đại Lê, Tuan Pham, Thi Hong Linh Nguyen, N. Tran, V. Dang
{"title":"Study On Some Matrix Equations Involving The Weighted Geometric Mean and Their Application","authors":"Xuân Đại Lê, Tuan Pham, Thi Hong Linh Nguyen, N. Tran, V. Dang","doi":"10.29007/7sj7","DOIUrl":"https://doi.org/10.29007/7sj7","url":null,"abstract":"In this paper we consider two matrix equations that involve the weighted geometric mean. We use the fixed point theorem in the cone of positive definite matrices to prove the existence of a unique positive definite solution. In addition, we study the multi-step stationary iterative method for those equations and prove the corresponding convergence. A fidelity measure for quantum states based on the matrix geometric mean is introduced as an application of matrix equation.","PeriodicalId":149532,"journal":{"name":"Kalpa Publications in Engineering","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129987416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}