Study On Some Matrix Equations Involving The Weighted Geometric Mean and Their Application

12 pages•Published: January 16, 2022

Xuan Dai Le, Tuan Cuong Pham, Thi Hong Van Nguyen, Nhat Minh Tran and Van Vinh Dang

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.

Keyphrases: fidelity measure for quantum states., fixed point theorem, matrix equations, multi step stationary iterative method, positive definite matrices, weighted geometric mean

In: Tich Thien Truong, Trung Nghia Tran, Thanh Nha Nguyen and Quoc Khai Le (editors). Proceedings of International Symposium on Applied Science 2021, vol 4, pages 50-61.

Links:	https://easychair.org/publications/paper/HGjG
	https://doi.org/10.29007/7sj7

BibTeX entry

@inproceedings{ISAS2021:Study_Some_Matrix_Equations,
  author    = {Xuan Dai Le and Tuan Cuong Pham and Thi Hong Van Nguyen and Nhat Minh Tran and Van Vinh Dang},
  title     = {Study On Some Matrix Equations Involving The Weighted Geometric Mean and Their Application},
  booktitle = {Proceedings of International Symposium on Applied Science 2021},
  editor    = {Tich Thien Truong and Trung Nghia Tran and Thanh Nha Nguyen and Quoc Khai Le},
  series    = {Kalpa Publications in Engineering},
  volume    = {4},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1770},
  url       = {/publications/paper/HGjG},
  doi       = {10.29007/7sj7},
  pages     = {50-61},
  year      = {2022}}

Download PDF Open PDF in browser