Arealn×nsymmetricmatrixX=(x_(ij))_(n×n)iscalledabisymmetricmatrixifx_(ij)=x_(n+1-j,n+1-i).Basedontheprojectiontheorem,thecanonicalcorrelationde-compositionandthegeneralizedsingularvaluedecomposition,amethodusefulforfindingtheleast-squaressolutionsofthematrixequationA~TXA=Boverbisymmetricmatricesisproposed.Theexpressionoftheleast-squaressolutionsisgiven.Moreover,inthecorrespondingsolutionset,theoptimalapproximatesolutiontoagivenmatrixisalsoderived.Anumericalalgorithmforfindingtheoptimalapproximatesolutionisalsodescribed.
