EXISTENCE AND UNIQUENESS OF DECOMPOSED SUM OF SYMMETRIC AND ORTHOGONAL PARTS FOR A REAL SQUARE MATRIX

The decomposition principle of an n-square matrix decomposed into a sum of a symmetric part and an orthogonal part was proved. For any n-square matrix, it can be decomposed into a sum of a symmetric matrix and an orthogonal matrix uniquely under some conditions. In general, it can be decomposed into constant multiple sum of a symmetric matrix and an orthogonal matrix uniquely.