行(列)对称矩阵的Schur分解和正规阵分解

Schur factorization and normal matrices factorization of row(column) symmetric matrices

提出了行(列)转置矩阵与行(列)反对称矩阵的概念,研究了它们的性质,获得了一些新的结果,给出了行(列)对称矩阵的Schur分解与正规阵分解的公式,它们可极大地减少行(列)对称矩阵的Schur分解与正规阵分解的计算量与存储量.

The concept of row （column） transposed matrix and row （column） synunetric matrix were given, and their basic properties were also studied. The formula for the Schur factorization and normal matrix factorization of row （column） symmetric matrix were obtained, all of which can dramatically reduce the amount of calculation and Schur factorization and normal matrix factorization of row （column） symmetric matrix can dramatically save the CPU time and memory without losing any numerical precision.