# IJPAM: Volume 52, No. 5 (2009)

**THE ANTI-BISYMMETRIC MATRICES OPTIMAL**

APPROXIMATION SOLUTION OF

MATRIX EQUATION

APPROXIMATION SOLUTION OF

MATRIX EQUATION

College of Mathematical Physics and Information Sciences

Xinjiang Normal University

Urumqi, Xinjiang, 830054, P.R. CHINA

e-mail: liaoyuan1126@163.com

e-mail: zcm19940809@sina.com

College of Mathematics and System Sciences

Xinjiang University

Urumqi, Xinjiang, 830046, P.R. CHINA

e-mail: znz01@xju.edu.cn

**Abstract.**This paper is mainly concerned with solving the following two problems:

**Problem I.** Given real matrices and , find
such that

**Problem II.** Given an real matrix , find an matrix such that
, where is a Frobenius norm, and is the solution set of Problem I.

The necessary
and sufficient conditions for the existence and expressions of the
general solutions of Problem I are given. The explicit solution, a
numerical algorithm and a numerical example to Problem
II are provided.

**Received: **May 15, 2008

**AMS Subject Classification: **15A52

**Key Words and Phrases: **anti-bisymmetric matrices, anti-symmetric matrix, Frobenius norm, optimal approximation

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 52

**Issue:** 5