A Numerical Value Index Applied to Diagnosis of Ill-conditioning Problems:Orthogonal Degree of Matrices

Based on the conception of the matrix volume,we presented the definition of the orthogonal degree of the matrices,generalized and extended the determinant method mentioned above.As the orthogonal degree of the matrices was applied to the ill-conditioning problems diagnostics,it is applicable to any matrices,and overcomes the drawbacks of the determinant method.