实方阵的对称与正交和分裂的存在性与惟一性

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

证明了n阶实方阵的对称与正交和分裂定理 ,即在一定条件下 ,一个实方阵可以惟一地分裂成一个对称矩阵与一个正交矩阵之和 ,在更一般意义下 ,可惟一地分裂成一个对称矩阵与一个正交矩阵的常数倍之和。

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.